University of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Fractional Ostrowski-type Inequalities via $(\alpha,\beta,\gamma,\delta)-$convex Function12070465310.22130/scma.2022.546225.1040ENAliHassanDepartment of Mathematics, Shah Abdul Latif University Khairpur-66020, Pakistan.0000-0003-1648-337XAsifR. KhanDepartment of Mathematics, University of Karachi, University Road, Karachi-75270, Pakistan.NaziaIrshadDepartment of Basic Sciences, Mathematics and Humanities, Dawood University of Engineering and Technology, M. A Jinnah Road, Karachi-74800, Pakistan.SumbulKhatoonDepartment of Mathematics, University of Karachi, University Road, Karachi-75270, Pakistan.Journal Article20220105In 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.https://scma.maragheh.ac.ir/article_704653_02efa3035f17bdc4a68255bcce4caaf5.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Results on Discontinuity at Fixed Point for a New Class of $F$-Contractive Mappings213270492010.22130/scma.2023.560141.1161ENPradipDebnathDepartment of Applied Science and Humanities, Assam University, Silchar, Cachar, Assam - 788011, India.0000-0003-0097-0819Journal Article20220813The 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, we aim to provide another new solution direction for the discontinuity study 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.https://scma.maragheh.ac.ir/article_704920_1890b3191389aa839fc3a86886cf532f.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Further Operator and Norm Versions of Young Type Inequalities334670508210.22130/scma.2023.562013.1174ENLeilaNasiriDepartment of Mathematics and computer science, Faculty of science, Lorestan University, Khorramabad, Iran.
Khorramabad, Iran.niversityMehdiShamsDepartment of Statistics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran.0000-0002-9645-9195Journal Article20220912In 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.https://scma.maragheh.ac.ir/article_705082_848560e073c418c5a44153be2bd0f1ca.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901On Relative Reproducing Kernel Banach Spaces: Definitions, Semi-Inner Product and Feature Maps476170534410.22130/scma.2023.1989152.1253ENMohammadrezaForoutanDepartment of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.Journal Article20230204In 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 in terms of the feature maps and establish the separability of the domains when they are separable. In addition, we prove some theorems concerning feature maps and reproducing kernel Banach spaces. And finally, the relative kernels are compared with the semi-inner ones.https://scma.maragheh.ac.ir/article_705344_4ede8aaddec68bebb5ad6d5865566b54.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Existence and Asymptotic of Solutions for a $p$-Laplace Schrödinger Equation with Critical Frequency638670580610.22130/scma.2023.1986209.1232ENJuanMayorga-ZambranoDepartment of Mathematics, Yachay Tech University, Hda. San Jos\'e s/n y Proyecto Yachay, Urcuqu\'i 100119, Ecuador.0000-0002-5714-3577JuanBurbano-GallegosTechnische Universitat Wien,
Wiedner Hauptstr. 8, 1040 Wien, Austria0000-0002-2410-5531BryanPerez-PilcoYachay Tech University, Hda. San Jose s/n y Proyecto Yachay, Urcuqui 100119, Ecuador.0000-0003-0288-5829JosueCastillo-JaramilloEötvös University, Pazmany Peter setany 1/C, 1117 Budapest, Hungary.0000-0002-5852-9594Journal Article20221231We study the Schr\"odinger equation $\left(\mathrm{Q}_{\varepsilon}\right)$: $- \varepsilon^{2(p-1)} \Delta_p v + V(x)\, |v|^{p-2} v - |v|^{q-1}v = 0$, $x \in \mathbb{R}^N$, 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, $\displaystyle \{x\in \mathbb{R}^N \, / \: V(x) = \inf V = 0\} \neq \emptyset$. 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 that for $\left(\mathrm{Q}_{\varepsilon}\right)$ there exists a non-trivial solution with any prescribed $\mathrm{L}^{q+1}$-mass.<br />Applying a Ljusternik-Schnirelman scheme, shows that $\left(\mathrm{Q}_{\varepsilon}\right)$ 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 $\left(\mathrm{P}\right)$ so that the critical values of the functionals associated, respectively, to $\left(\mathrm{Q}_{\varepsilon}\right)$ and $\left(\mathrm{P}\right)$ are topologically equivalent.https://scma.maragheh.ac.ir/article_705806_d70c440ea4b54a4025d40a50885779b0.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Inverse Conformable Sturm-Liouville Problems with a Transmission and Eigen-Parameter Dependent Boundary Conditions8710470752510.22130/scma.2023.2000439.1297ENMohammadShahriariDepartment of Mathematics, Faculty of Science, University of Maragheh, P.O. Box 55136-553, Maragheh, Iran.0000-0002-8982-2451RezaAkbariDepartment of Mathematical Sciences, Payame Noor University, Iran.0000-0000-0000-0000Journal Article20230418In this paper, we provide a different uniqueness results for inverse spectral problems of conformable fractional Sturm-Liouville operators of order $\alpha$ ($0 < \alpha\leq 1$), with a 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, from the Weyl function, the spectral data and two spectra. Moreover, we can also extend Hald's theorem to the problem.https://scma.maragheh.ac.ir/article_707525_aafd716f583bfc4cdc6dbb878dbb855a.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Fuzzy $\mu^*$-Open Set and Fuzzy $\mu^*$-Continuous Function10511670580810.22130/scma.2023.1973748.1204ENPankajChettriDepartment of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University Majitar, Rangpoo East Sikkim, India.0000-0001-9092-1492BishalBhandariDepartment of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University Majitar, Rangpoo East Sikkim, India.0000-0003-0969-8620Journal Article20221118The prime goal of this article is to initiate the notion of fuzzy $\mu^*$-open(closed) sets and fuzzy $\mu^*$-continuous functions and characterize them. These concepts are defined in a fuzzy topological space in presence of a 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 fuzzy $\mu^*$-continuous functions are established.https://scma.maragheh.ac.ir/article_705808_827b0eda5f24f6238afd03acd622351c.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Hermite-Hadamard-Fejér Inequalities for Preinvex Functions on Fractal Sets11713770581010.22130/scma.2022.559225.1156ENSikanderMehmoodDepartment of Mathematics, Govt. Graduate College Sahiwal, Pakistan.0000-0002-4042-4399FizaZafarCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan.Journal Article20220727In 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 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 calculus<br />contexts 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.https://scma.maragheh.ac.ir/article_705810_db12fd4fd110f4c8600ebea8ad634928.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Some Results on Non-Archimedean Operators Theory13915470593810.22130/scma.2023.557102.1139ENJawadEttaybDepartment of Mathematics and Computer Science, Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz, B.P. 1796 Atlas, F\`es, Morocco.0000-0002-4819-943XJournal Article20220703In 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.https://scma.maragheh.ac.ir/article_705938_71aab438815c6c8c5a952b6564d9860d.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901A Fuzzy Solution of Fractional Differential Equations by Fuzzy Conformable Laplace Transforms15517070534910.22130/scma.2023.555318.1128ENAtimadHarirLaboratory of Mathematical Modeling and Economic Calculation, Hassan 1er University, Settat, Morocco.0000-0003-3603-9268SaidMellianiLaboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, B.P. 523, Beni Mellal,
Morocco.0000-0002-5150-1185L. SaadiaChadliLaboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, B.P. 523, Beni Mellal, Morocco.0000-0002-5150-1185Journal Article20220607The fuzzy conformable Laplace transforms proposed in \cite{lp} are used to solve only fuzzy fractional differential equations of order $ 0 < \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 < \iota \leq 2$.https://scma.maragheh.ac.ir/article_705349_f243bb8e42dca32509c89399194a26a0.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Numerical Solution of Differential Equations of Elastic Curves in 3-dimensional Anti-de Sitter Space17118970657910.22130/scma.2022.556633.1135ENSamiraLatifiDepartment of Mathematics and Applications, Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran.NematAbazariDepartment of Mathematics and Applications, Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran.0000-0001-9101-6312GhaderGhasemiDepartment of Mathematics and Applications, Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran.0000-0001-9101-6312Journal Article20220627In this paper, we aim to extend the Darboux frame field into 3-dimensional Anti-de Sitter space and obtain two cases for this extension by considering a parameterized curve on a hypersurface; then we carry out the Euler-Lagrange equations and derive differential equations for non-null elastic curves in AdS$_{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.https://scma.maragheh.ac.ir/article_706579_acc051e72afb6c26018be66dbc062f29.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Generalized Ostrowski-Gruss Like Inequality on Time Scales19120370670910.22130/scma.2023.563178.1184ENFarazMehmoodDawood UniDepartment of Mathematics, Samarkand State University, University boulevard 15, Samarkand 140104, Uzbekistan and
Department of Mathematics, Dawood University of Engineering.Technology, New M. A. Jinnah Road, Karachi-74800, Pakistan.versity of Engineering and Technology.0000-0002-9536-3300Asif RazaKhanDepartment of Mathematics, University of Karachi, University Road, Karachi-75270 Pakistan.0000-0002-4700-4987Muhammad AwaisShaikhNabi Bagh Z. M. Govt. Science College, Saddar, Karachi-75270, Pakistan.0000-0002-5272-4452Journal Article20221009In 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 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.https://scma.maragheh.ac.ir/article_706709_f1de86517a5ad6ece0d4847e73234e37.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901Results via Partial-$b$ Metric and Solution of a Pair of Elliptic Boundary Value Problem20522570671010.22130/scma.2023.563638.1187ENAnitaTomarDepartment of Mathematics, Pt. L. M. S. Campus, Sridev Suman Uttarakhand University, Rishikesh-249201, Uttarakhand, India.0000-0001-8033-856XDeepakKumarDepartment of Mathematics,
Lovely Professional University, Phagwara, Punjab-144411, India.0000-0002-1028-5594RituSharmaG.I.C. Gheradhar (Dogi) Tehri Garhwal (Uttrakhand), India.MeenaJoshiDepartment of Mathematics, S. S. J. Campus, Soban Singh Jeena University Almora-263601, Uttarakhand, India.0000-0002-1562-0988Journal Article20221017We give a method to establish a fixed point via partial $b$-metric for multivalued mappings. 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 hypotheses to establish fixed circle/ disc theorems in a space that permits non-zero self-distance with a coefficient more significant than one. 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. 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.https://scma.maragheh.ac.ir/article_706710_c0125cadcfcb02e00975836a6597f88a.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901A Seneta's Conjecture and the Williamson Transform22724170671210.22130/scma.2023.1983415.1223ENEdwardOmeyDept. MEES, Campus Brussels, KU Leuven, Warmoesberg 26, Brussels, Belgium.0000-0002-9376-1188MeitnerCadenaDECE, Universidad de las Fuerzas Armadas, Sangolqui, Ecuador.0000-0002-0914-3740Journal Article20221226Considering slowly varying functions (SVF), %Seneta (2019) Seneta in 2019 conjectured the following implication, for $\alpha\geq1$,<br />$$<br />\int_0^x y^{\alpha-1}(1-F(y))dy\textrm{\ is SVF}\ \Rightarrow\ \int_{0}^x y^{\alpha}dF(y)\textrm{\ is SVF, as $x\to\infty$,}<br />$$<br />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.https://scma.maragheh.ac.ir/article_706712_1874b9e9f26269a43add982e3eaf0042.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580720420230901$G$-Frames Generated by Iterated Operators24326070580310.22130/scma.2023.1987650.1237ENMortezaRahmaniYoung Researchers and Elite Club, Ilkhchi Branch, Islamic Azad University, Ilkhchi, Iran.0000-0002-6505-6131Journal Article20230118Assuming that $\Lambda$ is a bounded operator on a Hilbert space $H$, this study investigate the structure of the $g$-frames generated by iterations of $\Lambda$. Specifically, we provide characterizations of $g$-frames in the form of $\{\Lambda^n\}_{n=1}^{\infty}$ and describe some conditions under which the sequence $\{\Lambda^n\}_{n=1}^{\infty}$ forms 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.https://scma.maragheh.ac.ir/article_705803_2c9e64d7597d2e9ed45cb9e120b0800e.pdf