Sahand Communications in Mathematical Analysis
https://scma.maragheh.ac.ir/
Sahand Communications in Mathematical Analysisendaily1Fri, 01 Sep 2023 00:00:00 +0430Fri, 01 Sep 2023 00:00:00 +0430Fractional Ostrowski-type Inequalities via $(\alpha,\beta,\gamma,\delta)-$convex Function
https://scma.maragheh.ac.ir/article_704653.html
In this paper, we are introducing for the first time a generalized class named the class of $(\alpha,\beta,\gamma,\delta)-$convex functions of mixed kind. This generalized class contains many subclasses including the class of $(\alpha,\beta)-$convex functions of the first and second kind, $(s,r)-$convex functions of mixed kind, $s-$convex functions of the first and second kind, $P-$convex functions, quasi-convex functions and the class of ordinary convex functions. In addition, we would like to state the generalization of the classical Ostrowski inequality via fractional integrals, which is obtained for functions whose first derivative in absolute values is $(\alpha,\beta,\gamma,\delta)-$ convex function of mixed kind. Moreover, we establish some Ostrowski-type inequalities via fractional integrals and their particular cases for the class of functions whose absolute values at certain powers of derivatives are $(\alpha,\beta,\gamma,\delta)-$ convex functions of mixed kind using different techniques including H\"older's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, the applications of special means will also be discussed.Results on Discontinuity at Fixed Point for a New Class of $F$-Contractive Mappings
https://scma.maragheh.ac.ir/article_704920.html
The search for contractive definitions which do not compel the mapping to be continuous at fixed points remained an open problem for a long time. Several solutions to this open problem have been obtained in last two decades. The current paper, &nbsp;we aim to provide another new solution direction for the discontinuity study &nbsp;at fixed points using $F$-contractive mappings in a complete metric space. Several consequences of those new results are also provided. This manuscript consists of three main parts. In the first part, the notion of $F$-contractive mappings has been described. In the second part, discontinuity at the fixed point assuming continuity of the composition has been investigated, whereas in the third part, discontinuity at a fixed point without assuming continuity of the composition has been illustrated.Further Operator and Norm Versions of Young Type Inequalities
https://scma.maragheh.ac.ir/article_705082.html
In this note, first the better refinements of Young and its reverse inequalities for scalars are given. Then, several operator and norm versions according to these inequalities are established.On Relative Reproducing Kernel Banach Spaces: Definitions, Semi-Inner Product and Feature Maps
https://scma.maragheh.ac.ir/article_705344.html
In this paper, a special class of relative reproducing kernel Banach spaces a semi-inner product is studied. We extend the concept of relative reproducing kernel Hilbert spaces to Banach spaces. We present these relative reproducing kernel Banach spaces &nbsp;in terms of the feature maps and establish the separability of the domains when they are &nbsp;separable. In addition, we prove some theorems concerning feature maps and reproducing kernel Banach spaces. And finally, the relative kernels are compared with the &nbsp;semi-inner ones.Existence and Asymptotic of Solutions for a $p$-Laplace Schrödinger Equation with Critical Frequency
https://scma.maragheh.ac.ir/article_705806.html
We study the Schr\"odinger equation&nbsp;&nbsp; $\left(\mathrm{Q}_{\varepsilon}\right)$: $- \varepsilon^{2(p-1)} \Delta_p v + V(x)\, |v|^{p-2} v - |v|^{q-1}v = 0$, $x \in \mathbb{R}^N$, with $v(x) \rightarrow 0$ as $|x| \rightarrow+\infty$, for the infinite case, as given by Byeon and Wang for a situation of critical frequency,&nbsp; $\displaystyle \{x\in \mathbb{R}^N \, / \: V(x) = \inf V = 0\} \neq \emptyset$. In the semiclassical limit, $\varepsilon \rightarrow 0$, the corresponding limit problem is $\left(\mathrm{P}\right)$: $\Delta_p w+|w|^{q-1} w=0$, $x \in \Omega$, with $w(x)=0, x \in \partial \Omega$, where $\Omega \subseteq \mathbb{R}^N$ is a smooth bounded strictly star-shaped region related to the potential $V$. We prove&nbsp; that for $\left(\mathrm{Q}_{\varepsilon}\right)$ there exists a non-trivial solution with any prescribed $\mathrm{L}^{q+1}$-mass.Applying a Ljusternik-Schnirelman scheme, shows &nbsp;that &nbsp;$\left(\mathrm{Q}_{\varepsilon}\right)$ and $\left(\mathrm{P}\right)$ have infinitely many pairs of solutions. Fixed a topological level $k \in \mathbb{N}$, we show that a solution of $\left(\mathrm{Q}_{\varepsilon}\right)$, $v_{k, \varepsilon}$, sub converges, in $\mathrm{W}^{1,p}(\mathbb{R}^N)$ and up to scaling, to a corresponding solution of $\left(\mathrm{P}\right)$. We also prove that the energy of each solution, $v_{k,\eps}$ converges to the corresponding energy of the limit problem&nbsp; $\left(\mathrm{P}\right)$ so that the critical values of the functionals associated, respectively, to&nbsp; $\left(\mathrm{Q}_{\varepsilon}\right)$ and $\left(\mathrm{P}\right)$ are topologically equivalent.Inverse Conformable Sturm-Liouville Problems with a Transmission and Eigen-Parameter Dependent Boundary Conditions
https://scma.maragheh.ac.ir/article_707525.html
In this paper, we provide a different &nbsp;uniqueness results for inverse spectral problems of conformable fractional Sturm-Liouville operators of order $\alpha$ ($0 &lt; \alpha\leq &nbsp;1$), with &nbsp;a &nbsp;jump and eigen-parameter dependent boundary conditions. Further, we study the asymptotic form of solutions, eigenvalues and the corresponding eigenfunctions of the problem. Also, we consider three terms of the inverse problem, &nbsp;from the Weyl function, &nbsp;the spectral data and &nbsp;two spectra. Moreover, we can also extend Hald's theorem to the problem.Fuzzy $\mu^*$-Open Set and Fuzzy $\mu^*$-Continuous Function
https://scma.maragheh.ac.ir/article_705808.html
The prime goal of this article is to initiate the notion of fuzzy &nbsp; &nbsp;$\mu^*$-open(closed) sets and fuzzy $\mu^*$-continuous functions and characterize &nbsp;them. These concepts are defined in a fuzzy topological space in presence of a &nbsp;generalized fuzzy topology, which becomes a new tool to study fuzzy topological spaces. It is observed that this class of fuzzy sets fail to form a fuzzy topology but it form a generalized fuzzy topology. Furthermore, the relationship of these fuzzy sets and fuzzy continuity with some existing fuzzy notions are established. Also the notion of fuzzy $(\tau, \mu^*)$-open(closed) functions is introduced and their equivalent conditions with &nbsp;fuzzy $\mu^*$-continuous functions are established.Hermite-Hadamard-Fejér Inequalities for Preinvex Functions on Fractal Sets
https://scma.maragheh.ac.ir/article_705810.html
In this paper, for generalised preinvex functions, new estimates of the Fej\'{e}r-Hermite-Hadamard inequality on fractional sets $\mathbb{R}^{\rho }$ are given in this study. We demonstrated a fractional &nbsp;integral inequalities based on Fej\'{e}r-Hermite-Hadamard theory. We establish two new local fractional integral identities for differentiable functions. We construct several novel Fej\'{e}r-Hermite-Hadamard-type inequalities for generalized convex function in local fractional calculuscontexts using these integral identities. We provide a few illustrations to highlight the uses of the obtained findings. Furthermore, we have also given a few examples of new inequalities in use.Some Results on Non-Archimedean Operators Theory
https://scma.maragheh.ac.ir/article_705938.html
In this paper, we define the notions of semi-regular operator, analytical core, surjectivity modulus and the injectivity modulus of bounded linear operators on non-Archimedean Banach spaces over $\mathbb{K}.$ We give a necessary and sufficient condition on the range of bounded linear operators to be closed. Moreover, many results are proved.A Fuzzy Solution of Fractional Differential Equations by Fuzzy Conformable Laplace Transforms
https://scma.maragheh.ac.ir/article_705349.html
The fuzzy conformable Laplace transforms proposed in \cite{lp} are used to solve only fuzzy fractional differential equations of order $ 0 &lt; \iota \leq 1$. In this article, under the generalized conformable fractional derivatives notion, we extend and use this method to solve fuzzy fractional differential equations of order $ 0 &lt; \iota \leq 2$.Numerical Solution of Differential Equations of Elastic Curves in 3-dimensional Anti-de Sitter Space
https://scma.maragheh.ac.ir/article_706579.html
In this paper, we aim to extend the Darboux frame field into 3-dimensional Anti-de Sitter space and obtain two cases for this extension by considering a parameterized curve on a hypersurface; then we carry out the Euler-Lagrange equations and derive differential equations for non-null elastic curves in AdS$_{3}$ (i.e. 3-dimensional Anti-de Sitter space). In this study, we investigate the elastic curves in AdS$_{3}$ and obtain equations through which elastic curves are found out. Therefore, we solve these equations numerically and finally plot and design some elastic curves.Generalized Ostrowski-Gruss Like Inequality on Time Scales
https://scma.maragheh.ac.ir/article_706709.html
In this paper, we present a generalization of the Montgomery Identity to various time scale versions, including the discrete case, continuous case, and the case of quantum calculus. By obtaining this generalization of Montgomery Identity &nbsp;we establish results about the generalization of Ostrowski-Gr\"{u}ss like inequality to the several time scales, namely discrete case, continuous case and the case of quantum calculus. Additionally, we recapture several published results from different authors in various papers, thus unifying the corresponding discrete and continuous versions. Furthermore, we demonstrate the applicability of our derived consequence to the case of quantum calculus.Results via Partial-$b$ Metric and Solution of a Pair of Elliptic Boundary Value Problem
https://scma.maragheh.ac.ir/article_706710.html
We give a &nbsp;method to establish a fixed point via partial $b$-metric &nbsp;for multivalued mappings. &nbsp;Since the geometry of multivalued fixed points perform a significant role in numerous real-world problems and is fascinating and innovative, we introduce the notions of fixed circle and fixed disc to frame &nbsp;hypotheses to establish fixed circle/ disc theorems in a &nbsp;space that permits non-zero self-distance with a coefficient more significant &nbsp;than one. &nbsp;Stimulated by the reality that the fixed point theorem is the frequently used technique for solving boundary value problems, we solve a pair of elliptic boundary value problems.&nbsp; Our developments cannot be concluded from the current outcomes in related metric spaces. Examples are worked out to substantiate the validity of the hypothesis of our results.A Seneta's Conjecture and the Williamson Transform
https://scma.maragheh.ac.ir/article_706712.html
Considering slowly varying functions (SVF), %Seneta (2019) Seneta in 2019 conjectured the following implication, for $\alpha\geq1$,$$\int_0^x y^{\alpha-1}(1-F(y))dy\textrm{\ is SVF}\ \Rightarrow\ \int_{0}^x y^{\alpha}dF(y)\textrm{\ is SVF, as $x\to\infty$,}$$where $F(x)$ is a cumulative distribution function on $[0,\infty)$. By applying the Williamson transform, an extension of this conjecture is proved. Complementary results related to this transform and particular cases of this extended conjecture are discussed.$G$-Frames Generated by Iterated Operators
https://scma.maragheh.ac.ir/article_705803.html
Assuming that $\Lambda$ is a bounded operator on a Hilbert space $H$, this study investigate the structure of the $g$-frames generated by &nbsp;iterations of $\Lambda$. Specifically, we provide &nbsp;characterizations of $g$-frames &nbsp;in the form of $\{\Lambda^n\}_{n=1}^{\infty}$ and describe some conditions under which the sequence $\{\Lambda^n\}_{n=1}^{\infty}$ forms&nbsp; a $g$-frame for $H$. Additionally, we verify the properties of the operator $\Lambda$ when $\{\Lambda^n\}_{n=1}^{\infty}$ is a $g$-frame for $H$. Moreover, we study the $g$-Riesz bases and dual $g$-frames which are generated by iterations. Finally, we discuss the stability of these types of $g$-frames under some perturbations.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.Asymptotically 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.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 $k$.