Sahand Communications in Mathematical Analysis
https://scma.maragheh.ac.ir/
Sahand Communications in Mathematical Analysisendaily1Mon, 01 Jan 2024 00:00:00 +0330Mon, 01 Jan 2024 00:00:00 +0330Asymptotically Almost Periodic Generalized Ultradistributions and Application
https://scma.maragheh.ac.ir/article_707710.html
The paper aims to introduce and study an algebra of asymptotically almost periodic generalized ultradistributions. These generalized ultradistributions contain &nbsp;asymptotically almost periodic ultradistributions and asymptotically almost periodic generalized functions. The definition and main properties of these generalized ultradistributions are studied. An application to difference differential systems is given.Sitaru-Schweitzer Type Inequality for Fuzzy and Pseudo-Integrals
https://scma.maragheh.ac.ir/article_706267.html
In this paper, we have proved and stated the Sitaru-Schweitzer type inequality for fuzzy integrals and &nbsp;also we state this inequality for pseudo-integrals in two classes. The first one is for &nbsp;pseudo-integrals where pseudo-addition and pseudo-multiplication are constructed by a monotone continuous function $g:[0, \infty ]\to[0, \infty]$. Another one is given by the semiring $([a, b], \max, \odot)$ where an increasing function generates pseudo-multiplication.New Fixed Point Results for Some Rational Contraction on $(\phi , \psi)$-Metric Spaces
https://scma.maragheh.ac.ir/article_706752.html
In this article, we define &nbsp;generalized $(\varphi,\sigma,\gamma)$-rational contraction, generalized $(\alpha\beta,\varphi\theta,F)$-rational &nbsp;contraction &nbsp;and establish some new fixed &nbsp;point results in $(\phi,\psi)$-metric space. We also present instances to support our main results. We will use the results we obtained to investigate the existence and uniqueness of solutions to first-order differential equations.Quaternion Hankel Transform and its Generalization
https://scma.maragheh.ac.ir/article_706754.html
In this study, the quaternion Hankel transform is developed. Basic operational properties and inversion formula of quaternion Hankel transform are derived. Parseval&rsquo;s relation for this transform is also established. The generalized quaternion Hankel transform is presented. In the concluding section, we demonstrate the application of the quaternion Hankel transform to Cauchy&rsquo;s problem.A Gradient Bound for the Allen-Cahn Equation Under Almost Ricci Solitons
https://scma.maragheh.ac.ir/article_706806.html
In this paper, we consider positive solutions for the Allen-Cahn equation\begin{equation*}\Delta u+\left(1-u^{2}\right)u=0,\end{equation*}on an almost Ricci soliton &nbsp; without a boundary. Firstly, using volume comparison Theorem and Sobolev inequality, we estimate the upper bound of $\vert \nabla u\vert^{2}$. As one of the applications, we extend this result to a gradient Ricci almost soliton. Finally, we obtain a Liouville-type theorem for almost Ricci solitons.Ternary Generalized Jordan Ring Homomorphisms on Ternary Non-Archimedean Banach Algebras
https://scma.maragheh.ac.ir/article_706813.html
In this paper, we introduce the notion of the ternary generalized Jordan ring homomorphism on ternary non-Archimedean Banach algebras. Utilizing &nbsp;alternative fixed point methods, we establish the generalized Hyers-Ulam stability of ternary generalized Jordan ring homomorphisms on ternary non-Archimedean Banach algebras associated with the generalized additive functions in several variables.Fractional Ostrowski Type Inequalities via $\phi-\lambda-$Convex Function
https://scma.maragheh.ac.ir/article_707159.html
In this paper, we aim to &nbsp;state well-known Ostrowski inequality via fractional Montgomery identity for the class of $\phi-\lambda-$ convex functions. This generalized class of convex function contains other well-known convex functions from literature, allowing us to derive Ostrowski-type inequalities as specific instances. Moreover, we present Ostrowski-type inequalities for which certain powers of absolute derivatives are $\phi-\lambda-$ convex using various techniques, including H&ouml;lder's inequality and the power mean inequality. Consequently, various established results would be captured as special cases. Moreover, we provide applications in terms of special means, allowing us to derive many numerical inequalities related to special means from Ostrowski-type inequalities.$f_{\delta}$-Open Sets in Fine Topological Spaces
https://scma.maragheh.ac.ir/article_707569.html
In this paper, the concept of $\delta$-cluster point on a set which belongs to the collection of fine open sets generated by the topology $\tau$ on $X$ has been introduced. Using this definition, the idea of $f_\delta$-open sets is initiated and certain properties of these sets have &nbsp;also been studied. On the basis of separation axioms defined over fine topological space, certain types of $f_\delta$-separation axioms on fine space have also been &nbsp;defined, along with some illustrative examples.Certain Properties Associated with Generalized $M$-Series using Hadamard Product
https://scma.maragheh.ac.ir/article_707702.html
The generalized $M$-series is a hybrid function of generalized Mittag-Leffler function and generalized hypergeometric function. &nbsp;The principal aim of this paper is to investigate certain properties resembling those of the Mittag-Leffler and Hypergeometric functions including various differential and integral formulas associated with generalized $M$-series. Certain corollaries involving the generalized hypergeometric function are also discussed. Further, in view of Hadamard product of two analytic functions, we have represented &nbsp;our main findings in Hadamard product of two known functions.Novel Optimal Class of Eighth-Order Methods for Solving Nonlinear Equations and Their Dynamical Aspects
https://scma.maragheh.ac.ir/article_707991.html
In this paper, a novel optimal class of eighth-order convergence methods for finding simple roots of nonlinear equations is derived based on the Predictor-Corrector of Halley method. By combining weight functions and derivative approximations, &nbsp;an optimal class of iterative methods with eighth-order convergence is constructed. In terms of computational cost, the proposed methods require three function evaluations, and the first derivative is evaluated once per iteration. Moreover, the methods have efficiency indices equal to 1.6817. The proposed methods have been tested with several numerical examples, as well as a comparison with existing methods for analyzing efficacy is presented.A Study on a Fractional q-Integro-Differential Inclusion by Quantum Calculus with Numerical and Graphical Simulations
https://scma.maragheh.ac.ir/article_707992.html
In this paper, we investigate the existence of a solution for the fractional q-integro-differential inclusion with new double sum and product boundary conditions. One of the most recent techniques of fixed point theory, i.e. endpoints property, and inequalities, plays a central role in proving the main results. For a better understanding of the issue and validation of the results, we presented numerical algorithms, tables and some figures. The paper ends with an example.Rigidity of Weak Einstein-Randers Spaces
https://scma.maragheh.ac.ir/article_707993.html
The Randers metrics are popular metrics similar to the Riemannian metrics, frequently used in physical and geometric studies. The weak Einstein-Finsler metrics are a natural generalization of the Einstein-Finsler metrics. Our proof shows that if $(M,F)$ is a simply-connected and compact Randers manifold and $F$ is a weak Einstein-Douglas metric, then every special projective vector field is Killing on $(M,F)$. Furthermore, we demonstrate that if a connected and compact manifold $M$ of dimension $n \geq 3$ admits a weak Einstein-Randers metric with Zermelo navigation data $(h,W)$, then either the $S$-curvature of $(M,F)$ vanishes, or $(M,h)$ is isometric to a Euclidean sphere ${\mathbb{S}^n}(\sqrt{k})$, with a radius of $1/\sqrt{k}$, for some positive integer $k$.General Fractional Integro-Differential Equation of Order $\varrho\in(2,3]$ Involving Integral Boundary Conditions
https://scma.maragheh.ac.ir/article_708317.html
In this paper, we are interested in studying an integro-differential equation with two-point integral boundary conditions using &nbsp;the Caputo fractional derivative of order $2&lt; \varrho \leq 3$. The considered problem is transformed into an equivalent integral equation. To study existence and uniqueness results, our approaches used is based on two well-known fixed point theorems, Banach contraction and Krasnoselskii's theorems. To illustrate our obtained outcomes, an example is given at the end of this paper.Infinitely Many Fast Homoclinic Solutions for Damped Vibration Systems with Combined Nonlinearities
https://scma.maragheh.ac.ir/article_708349.html
This article &nbsp;concerns the existence of fast homoclinic solutions for the following damped vibration system\begin{equation*}\frac{d}{dt}(P(t)\dot{u}(t))+q(t)P(t)\dot{u}(t)-L(t)u(t)+\nabla W(t,u(t))=0,\end{equation*}where $P,L\in C\left(\mathbb{R},\mathbb{R}^{N^{2}}\right)$ are symmetric and positive definite matrices, $q\in C\left(\mathbb{R},\mathbb{R}\right)$ and $W\in C^{1}\left(\mathbb{R}\times\mathbb{R}^{N},\mathbb{R}\right)$. Applying the Fountain Theorem and Dual Fountain Theorem, we prove the above system possesses two different sequences of fast homoclinic solutions when $L$ satisfies a new coercive condition and the potential $W(t,x)$ is combined nonlinearity.Common Solution for a Finite Family of Equilibrium Problems, Inclusion Problems and Fixed Points of a Finite Family of Nonexpansive Mappings in Hadamard Manifolds
https://scma.maragheh.ac.ir/article_708413.html
In this paper, we present an iterative algorithm and prove that the sequence generated by this algorithm converges strongly to a common solution of a finite family of equilibrium problems, the quasi-variational inclusion problem and &nbsp;the set of common fixed points of a countable family of nonexpansive mappings.Bi-Univalent Functions of Complex Order Defined by Hohlov Operator Associated with $(\mathcal {P,Q})-$Lucas Polynomial
https://scma.maragheh.ac.ir/article_708512.html
On this study, two new subclasses of the function class $\Xi$ of bi-univalent functions of complex order defined in the open unit disc are introduced and investigated. These subclasses are connected to the Hohlov operator with $(\mathcal {P,Q})-$Lucas polynomial and meet subordinate criteria. For functions in these new subclasses, we also get estimates for the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. The results are also discussed as having a number of (old or new) repercussions.Graphical Cyclic $\mathcal{K}$-Quasi-Contractive Mappings and the Existence of their Best Proximity Points
https://scma.maragheh.ac.ir/article_709585.html
The underlying aim of this paper is first to state the Cyclic version of $\mathcal{K}$-quasi-contractive mappings introduced by Fallahi and Aghanians [On quasi-contractions in metric spaces with a graph, Hacet. J. Math. Stat. 45 (4) (2016), 1033-1047]. Secondly, it seeks to show to show the existence of fixed point and best proximity points for such contractive mappings in a metric space with a graph, which can entail a large number of former fixed point and best proximity point results. One fundamental issue that can be distinguished between this work and previous studies is that it can also involve all of results stated by taking comparable and $\eta$-close elements.Generalized Niezgoda's Inequality with Refinements and Applications
https://scma.maragheh.ac.ir/article_708584.html
Motivated by the results of Niezgoda, corresponding to the generalization of Mercer's inequality for positive weights, in this paper, we consider real weights, for which we establish related results. To be more specific, Niezgoda's results are derived under Jensen Steffensen conditions. In addition, we construct some functionals enabling us to refine Niezgoda's results. Lastly, we discuss some applications.Statistical Deferred Weighted Riemann Summability and Fuzzy Approximation Theorems
https://scma.maragheh.ac.ir/article_708587.html
The notion of statistical convergence has fascinated many researchers due mainly to the fact that it is more general than the well-established hypothesis of ordinary (classical) convergence. This work aims to investigate and present (presumably new) the statistical versions of deferred weighted Riemann integrability and deferred weighted Riemann summability for sequences of fuzzy functions. We first interrelate these two lovely theoretical notions by establishing an inclusion theorem. We then state and prove two fuzzy Korovkin-type theorems based on our proposed helpful and potential notions. We also demonstrate that our results are the nontrivial extensions of several known fuzzy Korovkin-type approximation theorems given in earlier works. Moreover, we estimate the statistically deferred weighted Riemann summability rate supported by another promising new result. Finally, we consider several interesting exceptional cases and illustrative examples supporting our definitions and the results presented in this paper.Basis of Fuzzy Generalized Topological Space
https://scma.maragheh.ac.ir/article_708414.html
This paper studies the concept of fuzzy generalized topologies, which are generalizations of smooth topologies and Chang's fuzzy topologies. A basis of fuzzy generalized topological space will be defined as functions from the family of all fuzzy subsets of a non-empty set $ X $ to $ [0, 1] $ and &nbsp;some basic properties of their structure will be obtained. Some characterizations of &nbsp;the basis of fuzzy generalized topology, fuzzy generalized cotopology and the product of fuzzy generalized topological spaces will also be shown.On Some New Classes of $\mathcal{I}-$Convergent Sequences in GNLS
https://scma.maragheh.ac.ir/article_708513.html
This paper is devoted to study $\mathcal{I}$-convergent,$\mathcal{I-}$null, $\mathcal{I-}$bounded and bounded sequence spaces in gradual normed linear spaces, denoted by $c_{\| \cdot \|_G} ^\mathcal{I} ,c_{0 \| \cdot \|_G} ^\mathcal{I} ,\ell_{\infty \| \cdot \|_G} ^\mathcal{I}, \ell_{\infty \| \cdot\|_G}, m_{\| \cdot \|_G} ^\mathcal{I}$ and $m_{0 \| \cdot \|_G} ^\mathcal{I}$ respectively. We discussed some algebraic and topological properties of these classes. Also, we studied some inclusions involving these spaces.Generalized Fractional Integral Inequalities for $(h,m,s)$-Convex Modified Functions of Second Type
https://scma.maragheh.ac.ir/article_708589.html
New variants of the Hermite - Hadamard inequality within the framework of generalized fractional integrals for $(h,m,s)$-convex modified second type functions have been obtained in this article. To achieve these results, we used the Holder inequality and another form of it - power means. Some of the known results described in the literature can be considered as particular cases of the results obtained in our study.Some New Results for the $\mathscr{M}$-Transform Involving the Incomplete $I$-Functions
https://scma.maragheh.ac.ir/article_708783.html
Integral transformations are crucial for solving a variety of actual issues. The right choice of integral transforms aids in simplifying both integral and differential problems into a solution-friendly algebraic equation. In this paper, $\mathscr{M}$-transform is applied to establish the image formula for the multiplication of a family of polynomials and incomplete $I$-functions. Additionally, we discovered image formulations for a few significant and valuable cases of incomplete $I$-functions. Numerous previously unknown and novel conclusions can be reached by assigning specific values to the parameters involved in the primary conclusions drawn in this study.Some Properties of Close-To-Convex Functions Associated with A Strip Domain
https://scma.maragheh.ac.ir/article_708845.html
Using subordination, we introduce a new class of symmetric functions associated with a vertical strip domain. We have provided some interesting deviations or adaptation which are helpful in unification and extension of various studies of analytic functions. Inclusion relations, geometrical interpretation, coefficient estimates, inverse function coefficient estimates and solution to the Fekete-Szeg\H{o} problem of the defined class are our main results. &nbsp;Applications of our main results are given as corollaries.The Stability of Bi-Drygas Functional Equation
https://scma.maragheh.ac.ir/article_709134.html
In this paper, we introduce and solve a system of bi-Drygas functional equations&nbsp;\begin{equation}\left\{\begin{aligned}&nbsp; &nbsp; &nbsp; &nbsp; &amp;f(x+y,z)+f(x-y,z)=2f(x,z)+f(y,z)+f(-y,-z)\nonumber\\&nbsp; &nbsp; &nbsp; &nbsp; &amp;f(x,y+z)+f(x, y-z)=2f(x,y)+f(x,z)+f(-x,-z)\nonumber\end{aligned}\right.\end{equation}for all $x,y,z\in X$. We will also investigate the Hyers-Ulam stability of the system of bi-Drygas functional equations.On Saigo Fractional $q$-Calculus of a General Class of $q$-Polynomials
https://scma.maragheh.ac.ir/article_709281.html
In this paper, we derive Saigo fractional $q$-integrals of the general class of $q$-polynomials and demonstrate their application by investigating $q$-Konhouser biorthogonal polynomial, &nbsp;$q$-Jacobi polynomials and basic analogue of the Kamp$\acute{e}$ de F$\acute{e}$riet function. We have also derived polynomials as a specific example of our significant findings.Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules
https://scma.maragheh.ac.ir/article_709282.html
In the present paper, we introduce &nbsp;the generalized inverse operators, which have an exciting role in operator theory. We establish Douglas' factorization theorem type &nbsp;for &nbsp;the Hilbert pro-$C^{\ast}$-module.We introduce the notion of atomic system and $K$-frame in the Hilbert pro-$C^{\ast}$-module and study their relationship. We also demonstrate some properties of the $K$-frame by using Douglas' factorization theorem.Finally &nbsp;we demonstrate that the sum of two $K$-frames in a Hilbert pro-$C^{\ast}$-module with certain conditions is once again a $K$-frame.New Subclass of Convex Functions Concerning Infinite Cone
https://scma.maragheh.ac.ir/article_709283.html
We introduce a new subclass of convex functions as follows:\[&nbsp; \mathcal{K}_{IC}:=\left\{f\in \mathcal{A}:{\rm&nbsp; Re}\left(1+\frac{zf''(z)}{f'(z)}\right)&gt;\left|f'(z)-1\right|,\quad&nbsp; |z|&lt;1\right\},\]where $\mathcal{A}$ denotes the class of analytic and normalized functions in the unit disk $|z|&lt;1$. Some properties of this particular class, including subordination relation, integral representation, the radius of convexity, rotation theorem, sharp coefficients estimate and Fekete-Szeg\"{o} inequality associated with the $k$-th root transform, are investigated.Beta-Bazilevič Function
https://scma.maragheh.ac.ir/article_709284.html
In this paper, we introduce a relatively new class, $\mathcal{\mathcal{B}}_{1}^\beta(\alpha)$, namely the class of Beta-Bazilevi\v{c} function is generated by the function Bazilevi\v{c} $\mathcal{B}_{1}(\alpha)$. We introduce the class in question by constructing the Alpha-Convex function, $\mathcal{M}(\alpha)$, introduced by Miller et al. \cite{15}. Using Lemmas of function with positive real part, we were given a sharp estimate of coefficient problems. The coefficient problems to be solved are the modulus of initial coefficients $f$, the modulus of inverse coefficients $f^{-1}$, the modulus of the Logarithmic coefficients $\log \frac{f(z)}{z}$, the Fekete-Szeg\"{o} problem and the second Hankel determinant problem.Generalized Difference Lacunary Weak Convergence of Sequences
https://scma.maragheh.ac.ir/article_709285.html
In this paper, we introduce the concept of generalized difference lacunary weak convergence of sequences. Using the concept of difference operator, we have introduced some new classes of sequences. We investigated several of its algebraic and topological properties, such as solidness, symmetry and monotone. We gave appropriate examples and detailed discussions to validate our established &nbsp;failure instances and definitions. Further, we have established some inclusion relations of the introduced sequence spaces with other sequence spaces, in particularly with the weak Ces`aro summable sequences.&nbsp;Generalization of Banach Contraction Principle for Prešić’s Type Mappings in Soft Metric Spaces
https://scma.maragheh.ac.ir/article_709295.html
The objective of this paper is to highlight the idea of $k$-weakly and $2k$-weakly soft compatible mappings and their utilization in proving the main results. For this aim, we establish some fixed point results for the Pre\v{s}i\'{c}'s type contractive mappings in the context of soft metric spaces, when the set of the parameter is finite. Also we give an example to show that the condition of finiteness on the set of parameter can't be omitted. Some examples are given to support main findings of this article. Finally, an application of a soft version of BCP in iterated soft function systems is established.$\mathcal{T}_{M}$-Amenability of Banach Algebras
https://scma.maragheh.ac.ir/article_709618.html
We introduce the notions of $\mathcal{T}_{M}$-amenability and $\phi$-$\mathcal{T}_{M}$-amenability. Then, we characterize $\phi$-$\mathcal{T}_{M}$-amenability &nbsp;in terms of $WAP$-diagonals and $\phi$-invariant means. Some concrete cases are also discussed.Extensions of $\varphi$-Fixed Point Results via $w$-Distance
https://scma.maragheh.ac.ir/article_709663.html
In this paper, we obtain a $\varphi$-fixed point result concerning $w$-distance. There are three illustrative examples. In a separate section, we compare of the present result with that of the corresponding results prevalent in metric spaces and indicate certain new features obtained using $w$-distance. One such feature is that under certain circumstances, the fixed point can be a point of discontinuity, which is impossible in the metric case. We give an application to non-linear integral equations. The paper ends with a conclusion.A Study on Fixed Circles in $ \phi $-Metric Spaces
https://scma.maragheh.ac.ir/article_709664.html
Our present work is the extension of the line of research in the context of $\phi$-metric spaces. We introduce the notion of fixed circle and obtain suitable conditions for the existence and uniqueness of fixed circles for self mappings. Additionally, we present some figures and examples in support of our &nbsp;results.&nbsp;New Results for Some Intuitionistic Fuzzy Partial Functional Differential Equations with State-Dependent Delay
https://scma.maragheh.ac.ir/article_709665.html
In this research work, we investigate novel findings concerning the existence and uniqueness of intuitionistic fuzzy solutions for state-dependent delay intuitionistic fuzzy partial functional differential equations with local initial conditions in a new weighted intuitionistic fuzzy complete metric space under suitable assumptions. The main results of this paper are based on the Banach fixed point theorem. An illustrated example of our results is given with some numerical simulations for $\beta$-cuts of the intuitionistic fuzzy solutions.Exponential Convex Functions with Respect to $s$
https://scma.maragheh.ac.ir/article_709698.html
In this paper, we study the concept of exponential convex functions with respect to $s$ and prove Hermite-Hadamard type inequalities for the newly introduced this class of functions. In addition, we get some refinements of &nbsp; &nbsp;the Hermite-Hadamard (H-H) inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is exponential convex with respect to $s$. Our results coincide with the results obtained previously in special cases.Companion of Ostrowski Inequality for Multiplicatively Convex Functions
https://scma.maragheh.ac.ir/article_709700.html
The objective of this paper is to examine integral inequalities related to multiplicatively differentiable functions. Initially, we establish a novel identity using the two-point Newton-Cotes formula for multiplicatively differentiable functions. Using this identity, we derive Companion of Ostrowski's inequalities for multiplicatively differentiable convex mappings. The work also provides the results' applications.Study of Transitivity, Periodic Density and Sensitivity for Chaotic Non-Autonomous Fuzzified Dynamical System
https://scma.maragheh.ac.ir/article_709869.html
The present investigations focus on the mathematical analysis and investigation of non-autonomous discrete dynamical systems. A non-autonomous discrete dynamical system has been framework &nbsp;using the series technique map method to elaborate the relationships between the non-autonomous discrete dynamical system in the original (crisp) system and its g-fuzzified system. More specially, for the considered non-autonomous discrete dynamical system, the relationship between transitivity, weakly mixing, periodic density, and sensitive dependence on initial conditions have been examined.&nbsp;Notes about Quasi-Mixing Operators
https://scma.maragheh.ac.ir/article_709870.html
In this article, we introduce quasi-mixing operators and construct various examples. We prove that quasi-mixing operators exist on all finite-dimensional and infinite-dimensional &nbsp;Banach spaces. We also prove that an invertible operator $T$ is quasi-mixing if and only if $T^{-1}$ is quasi-mixing. We state some sufficient conditions &nbsp;under which an operator is quasi-mixing. Moreover, we prove that the direct sum of two operators is quasi-mixing if and only if any of them is quasi-mixing.On Continuous Frames in Hilbert $C^*$-Modules
https://scma.maragheh.ac.ir/article_709996.html
In the present paper, we study continuous frames in Hilbert $C^*$-modules and present some results of these frames. Next, we give the concept of dual continuous frames in Hilbert $C^*$-modules and investigate some properties of them. Also, by introducing the notion of the similarity of the continuous frames, characterizing it, and stating some of its properties, we refer to the investigation of the effect of similarity on the dual continuous frames in Hilbert $C^*$-modules.Coefficient Estimate and Fekete-Szeg\"{o} Problems for Certain New Subclasses of Bi-univalent Functions Defined by Generalized Bivariate Fibonacci Polynomial
https://scma.maragheh.ac.ir/article_710125.html
This article deals with two new subclasses of analytic and bi-univalent functions in the open unit disk, which is defined &nbsp;by applying subordination principle between analytic functions and the generalized Bivariate Fibonacci polynomials. Bounds for coefficients $\left|a_{2}\right|$ and $\left|a_{3}\right|$ of functions in these subclasses are estimated in terms of generalized Bivariate Fibonacci polynomials. In addition, the Fekete-Szeg\"{o} problem is handled for the members of these subclasses and several consequences and examples of the main results are presented. The results of article generalize some of the previously published papers in the literature.&nbsp;A New Class of Integrals Connected with Polynomials and Extended Generalized Mittag-Leffler Function
https://scma.maragheh.ac.ir/article_710259.html
The aim of the present investigation is to deal with integrals, which are connected with the extended generalized Mittag-Leffler function, Jacobi polynomial, and Bessel-Maitland function. Further, we are also considering the integral formulae, which involve various special functions. Interesting special cases of the main results are also considered. The results obtained here are general in nature and can presume numerous new integral formulae connecting the several types of polynomials.Application of Gegenbauer Polynomials with Two Variables to Bi-univalency of Generalized Discrete Probability Distribution Via Zero-Truncated Poisson Distribution Series
https://scma.maragheh.ac.ir/article_710537.html
The present study is unique in exploring bi-univalent functions, which has recently garnered attention from many researchers in Geometric Function Theory (GFT). The uniqueness lies in utilizing a generalized discrete probability distribution and a zero-truncated Poisson distribution combined with generalized Gegenbauer polynomials featuring two variables. We aim to obtain coefficient bounds, the classical Fekete-Szeg&ouml; inequality, and Hankel and Toeplitz determinants to generalize the probability of a gambler's ruin. Additionally, using the defined bi-univalent function classes contributes to the uniqueness of the obtained results.Non-Expansive Multi-Valued Mappings and Convexity in Fuzzy Metric Space
https://scma.maragheh.ac.ir/article_710539.html
In this article, we delve into the concept of convexity within fuzzy metric spaces and delve into their structural characteristics. We present several theorems concerning the existence of coincidence points in fuzzy convex metric spaces. Furthermore, we introduce the notion of star-shaped subsets within fuzzy convex metric spaces. Within these star-shaped subsets, we showcase various fixed point theorems for mappings of the non-expansive type that commute. In the final section, we expand the definition of fuzzy convex metric spaces and provide a significant example of such a space. Additionally, we uncover specific fixed point theorems applicable to multi-valued mappings that are non-expansive.On a General Conditional Cauchy Functional Equation
https://scma.maragheh.ac.ir/article_710730.html
Let $(G,+)$ be an abelian group and $Y$ &nbsp;a linear space over the field $\Bbb{F}\in\{\Bbb{R}, \Bbb{C}\}$. In this paper, we investigate the conditional Cauchy functional equation \[f(x+y)\neq af(x)+bf(y)\quad\Rightarrow \quad f(x+y)=f(x)+f(y),\quad x,y\in G,\] for functions $f:G\to Y$, where &nbsp;$a,b\in \Bbb{F}$ are fixed constants. The general solution and stability of this functional equation are described.Score-Valued Decision Making Models Based on Inverse Soft Matrices
https://scma.maragheh.ac.ir/article_711075.html
In this work, we introduce some useful concepts &nbsp;in soft set theory, such as $\overline{\alpha}$-inverse intersection and &nbsp;$\overline{\alpha}$-inverse union of inverse soft sets, together with &nbsp;the type soft $\overline{\alpha}$-upper, $\overline{\alpha}$-lower, $\overline{\alpha}$-intersection and $\overline{\alpha}$-union of inverse soft matrices. &nbsp;Our main contribution is of proposing a new decision-making method associated with &nbsp;inverse soft sets and inverse soft matrices.Fuzzy Normed Linear Spaces Generated By Linear Functionals
https://scma.maragheh.ac.ir/article_711076.html
For a nonzero normed linear space X, we will define some different classes of fuzzy norms on X generated by linear and bounded linear functionals. Also separate continuity of the elements within each class are investigated. The aim of this research is to introduce a source of examples and counterexamples in the field of fuzzy normed spaces.&nbsp;Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded Turning
https://scma.maragheh.ac.ir/article_711319.html
In this paper, we investigate for a sharp upper bound to certain generalized second Hankel determinant, the Zalcman conjecture and an upper bound for the third, fourth Hankel determinants for the class of multivalent analytic bounded turning functions. Further, we estimate an upper bound for third and fourth Hankel determinants with respect to two-fold and three-fold symmetric functions belongs to the same class. The practical tools applied in deriving of our main results are the coefficient inequalities of the Carath$\acute{e}$odory class $\mathcal{P}.$The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator
https://scma.maragheh.ac.ir/article_711323.html
A generalized integral operator of order $\alpha$ of a real function $f$ &nbsp;including a parameter set $P$, namely $K_P^\alpha f(t)$ has been introduced by O. P. &nbsp;Agrawal &nbsp;(Computers and Mathematics with Applications, 59 (2010) 1852--1864), which is a generalization of some important fractional integrals such as the Riemann-Liouville fractional integral. Using pseudo-analysis, this paper introduces a pseudo-operator integral of order $\alpha$ including a parameter set $P$ &nbsp;in a semiring $([a, b], \oplus, \odot)$, which is &nbsp;a generalization of &nbsp;$K_P^\alpha f(t)$. We also discuss some particular cases and we obtain the well-known H\"{o}lder's and Minkowski's &nbsp;inequalities &nbsp;for this kind of pseudo-operator integral. The results given in this paper provide a generalization of several inequalities obtained in earlier studies.Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population Model
https://scma.maragheh.ac.ir/article_711325.html
This paper studies a fractional biological population model involving the Caputo-Fabrizio fractional derivative. We establish the existence and uniqueness of the solution using Banach's fixed point theorem. Furthermore, we propose a new numerical algorithm called $\mathbb{J}$-decomposition method ($\mathbb{J}$-DM) which is a combined form of the $\mathbb{J}$-transform method and a new decomposition method to solve the proposed model. After the convergence analysis of the $\mathbb{J}$-DM, we provide three numerical examples to illustrate the results obtained. The numerical examples show that this method is easy to use and can give accurate results.