فهرست مطالب
Sahand Communications in Mathematical Analysis
Volume:21 Issue: 3, Summer 2024
 تاریخ انتشار: 1403/04/11
 تعداد عناوین: 25


Pages 119
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.
Keywords: Fuzzy Norm, Linear Space, Linear Functional, Separate Continuity 
Pages 2134The present investigations focus on the mathematical analysis and investigation of nonautonomous discrete dynamical systems. A nonautonomous discrete dynamical system has been framework using the series technique map method to elaborate the relationships between the nonautonomous discrete dynamical system in the original (crisp) system and its gfuzzified system. More specially, for the considered nonautonomous discrete dynamical system, the relationship between transitivity, weakly mixing, periodic density, and sensitive dependence on initial conditions have been examined.Keywords: NonAutonomous Discrete Dynamical System, $G$Fuzzification, Zadeh's Extension, Periodic Density, Transitivity, Sensitive Dependence On Initial Conditions

Pages 3553This article deals with two new subclasses of analytic and biunivalent functions in the open unit disk, which is defined by applying subordination principle between analytic functions and the generalized Bivariate Fibonacci polynomials. Bounds for coefficients $\lefta_{2}\right$ and $\lefta_{3}\right$ of functions in these subclasses are estimated in terms of generalized Bivariate Fibonacci polynomials. In addition, the FeketeSzeg\"{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.Keywords: BiUnivalent Function, Coefficient Estimates, FeketeSzeg, {O} Functional, Bivariate Fibonacci Polynomials

A New Class of Integrals Connected with Polynomials and Extended Generalized MittagLeffler FunctionPages 5564The aim of the present investigation is to deal with integrals, which are connected with the extended generalized MittagLeffler function, Jacobi polynomial, and BesselMaitland 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.Keywords: MittagLeffler Function, Jacobi Polynomial, Extended Beta Function, Wright Generalized Bessel Function

Pages 6588The present study is unique in exploring biunivalent 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 zerotruncated Poisson distribution combined with generalized Gegenbauer polynomials featuring two variables. We aim to obtain coefficient bounds, the classical FeketeSzegö inequality, and Hankel and Toeplitz determinants to generalize the probability of a gambler's ruin. Additionally, using the defined biunivalent function classes contributes to the uniqueness of the obtained results.Keywords: BiUnivalent Function, Gegenbauer Polynomials, Discrete Probability, Hankel, Toeplitz Determinants, ZeroTruncatedPoisson Series

Pages 89110In 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 starshaped subsets within fuzzy convex metric spaces. Within these starshaped subsets, we showcase various fixed point theorems for mappings of the nonexpansive 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 multivalued mappings that are nonexpansive.Keywords: PMSpaces, Fixed Point, Coincidence Points, NonExpansive Mappings, Convex Structure

Pages 111126In this work, we introduce some useful concepts in soft set theory, such as $\overline{\alpha}$inverse intersection and $\overline{\alpha}$inverse union of inverse soft sets, together with the type soft $\overline{\alpha}$upper, $\overline{\alpha}$lower, $\overline{\alpha}$intersection and $\overline{\alpha}$union of inverse soft matrices. Our main contribution is of proposing a new decisionmaking method associated with inverse soft sets and inverse soft matrices.Keywords: Inverse Soft Set, Inverse Soft Matrix, Restricted Inverse Soft Set, Decision Making

Pages 127146In 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 twofold and threefold 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 $\mathcal{P}.$Keywords: PValent Bounded Turning Function, Upper Bound, Hankel Determinant, Univalent Function, Carath´Eodory Function, Hypergeometric Function

The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of PseudoOperatorPages 147163A generalized integral operator of order $\alpha$ of a real function $f$ including a parameter set $P$, namely $K_P^\alpha f(t)$ has been introduced by O. P. Agrawal (Computers and Mathematics with Applications, 59 (2010) 18521864), which is a generalization of some important fractional integrals such as the RiemannLiouville fractional integral. Using pseudoanalysis, this paper introduces a pseudooperator integral of order $\alpha$ including a parameter set $P$ in a semiring $([a, b], \oplus, \odot)$, which is a generalization of $K_P^\alpha f(t)$. We also discuss some particular cases and we obtain the wellknown H\"{o}lder's and Minkowski's inequalities for this kind of pseudooperator integral. The results given in this paper provide a generalization of several inequalities obtained in earlier studies.Keywords: RiemannLiouville Fractional Integral, PseudoAnalysis, Semiring, H, {O}Lder's Inequality, Minkowski's Inequality

Pages 165196This paper studies a fractional biological population model involving the CaputoFabrizio 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.Keywords: Fractional Biological Population Model, CaputoFabrizio Fractional Derivative, Banach Space, JTransform, Decomposition Method

Pages 197211The variational inclusion problems are the generalizations of the variational inequality problems. First, it was noted by Hasounni and Moudafi in 1994. Afterwards, many researchers look into the problems and try to improve the catch, and then the theory of the variational inclusion problems is enriched from time to time. There were some specific ways of solving the systems of the problems and it is called the approximation solvability of the system, which was due to R. U. Verma in 2008. Here in this study, we investigate the approximation solvability of solutions for the system of generalized nonlinear ordered variational inclusions using an iterative algorithm under some apt conditions. We employ the resolvent operator techniques in our iterative scheme as a baseline. Some exceptional cases of the problem and iterative scheme are also discussed.Keywords: Solvability, GVIP, Approximation, Existence

Pages 213226The present work is an investigation of some new sequence spaces $c^{I}_{0}\left(C\right)$, $c^{I}\left(C\right)$, $\ell^{I}_{\infty}\left(C\right)$ and $\ell_{\infty}\left(C\right)$ as a domain of the triangle Copson matrix via ideal convergence over an admissible ideal of $\mathbb{N}$. Also, I will define some algebraic, topological properties and inclusion relations in these spaces.Keywords: Copson Matrix, Copson Ideal Convergence, Ideal Convergence, Ideal, Filter

Pages 227248We apply the RiemannLiouville fractional integral to generalize a companion of Ostrowski's type integral inequality. The present article recaptures all the results of M. W. Alomari's article and also for one more article of different authors. Applications are also deduced for numerical integration, probability theory and special means.Keywords: Fractional Calculus, RiemannLiouville Fractional Integral Operator, Ostrowski’S Inequality, Differentiable Mapping, Numerical Integration, Probability Density Function, Special Means

Pages 249266This paper is devoted to introduce a new concept of bases for the range of the operator $K$. Actually, we consider controlled $K$orthonormal and controlled $K$Riesz bases which are a generalization of ordinary bases in Hilbert spaces. In the sequel, we give some characterizations of these sequences. Next, we construct some new controlled bases with operator theory tools. Finally, some dual characterizations are given.Keywords: Controlled Frame, KFrame, Riesz Basis, Orthonormal Basis

Pages 267278In this study, we first establish two new identities for multiplicative differentiable functions. Based on these identities, we derive the midpoint and trapezoid type inequalities. The acquired outcomes improve and refine upon Khan and Budak's findings. At the conclusion, some applications to special means are provided.Keywords: NonNewtonian Calculus, Midpoint Inequality, Trapezoid Inequality, Multiplicatively Convex Functions

Pages 279300In this paper, it is aimed to improvement the boundaries of fractional integral operators containing extended generalized MittagLeffler functions. The offered results enhance the previously known bounds of the distinct fractional integral operators for strongly $p$convex functions of higher order. The acquired inequalities ensure boundedness, continuity, and Hadamard type inequality for fractional integrals containing an expanded MittagLeffler function. Furthermore, these results can be refined for various classes of strongly convex functions offered in the literature.Keywords: MittagLeffler Function, Strongly $P$Convexity Of Higher Order, $K$Fractional Integrals, Hadamard Inequality, Fej, 'ErHadamard Inequality

Pages 301322This paper explores the study of a specific category of nonlinear multipoint boundary value problems (BVPs) associated with RieszCaputo fractional differential equations and integral boundary conditions. The primary objective is to establish the existence of solutions under specific assumptions. We use Krasnoselskii's fixed point theorem and LeraySchauder's nonlinear alternative to achieve this goal. Furthermore, numerical examples are presented and plotted to demonstrate the effectiveness of the obtained results.Keywords: Existence Of Solutions, Fixed Point Theorem, RieszCaputo

Pages 323359In this study, we established the HermiteHadamard type, Simpson type, Ostrowski type and midpoint type integral inequalities for the sconvex functions in the second sense via Katugampola fractional integrals. By using Katugampola fractional integral operators, we obtained several new identities and presented new results for the sconvex function in the second sense. We made connections of our results with various results recognized in the literature. Finally, applications to special means are examined to verify the efficiency of the established results.Keywords: HermiteHadamard Type Inequalities, Simpson Type Inequalities, Ostrowski Type Inequalities, Holder's Inequality, Young's Inequality, SConvex Function, Katugampola Fractional Integral Operators, Special Means

Pages 361370In this paper, we verify some extra properties in quotient Banach lattices. Especially, we characterize the zero neighborhoods under unbounded norm topology (untopology) in quotient Banach lattices. We verify some types of convergence in a quotient Banach lattice. Also, we show that if a Banach lattice is atomic, then the quotient Banach lattice so is. Finally, we show that the quotient preserves Schur and BanachSaks properties.Keywords: Quotient Banach Lattice, UnTopology, Atom

Pages 371385The current paper discusses the global existence and asymptotic behavior of solutions of the following new nonlocal problem$$ u_{tt} M\left(\displaystyle \int_{\Omega}\nabla u^{2}\, dx\right)\triangle u + \delta u_{t}= u^{\rho2}u \logu, \quad \text{in}\ \Omega \times ]0,\infty[, $$where\begin{equation*}M(s)=\left\{\begin{array}{ll}{abs,}&{\text{for}\ s \in [0,\frac{a}{b}[,}\\{0,}&{\text{for}\ s \in [\frac{a}{b}, +\infty[.}\end{array}\right.\end{equation*}If the initial data are appropriately small, we derive existence of global strong solutions and the exponential decay of the energy.Keywords: Global Solutions, Degenerate Nonlocal Problem, Asymptotic Behavior

Pages 387416In this paper, we define strong deferred summability and deferred statistical summability in intuitionistic fuzzy \(n\)normed linear spaces (briefly called IF\(n\)NLS) and study some of their properties. We also define deferred statistical Cauchy sequence deferred statistical completeness and characterize deferred statistical summability in such spaces. Finally, we will compare deferred statistical summability for different pairs of sequences $\alpha(\ell)$, $\gamma(\ell)$,$u(\ell)$ and $v(\ell)$ satisfying $\alpha(\ell) \leq u(\ell) < v(\ell) \leq \gamma(\ell)$.Keywords: Statistical Summability, Deferred Statistical Summability, Deferred Statistical Cauchy Sequence, Deferred Statistical Completeness, Intuitionistic Fuzzy NNormed Linear Space

Pages 417429In this paper, we define and investigate $\mu^{*}$$R_{0}$ and $\mu^{*}$$R_{1}$ spaces in a generalized topological space together with a topology. Independence of these spaces from the existing allied concepts is shown by examples, which motivates to explore them further. It is interesting to note that $(\mu X, \mu Y)$continuous image of $\mu^{*}$$R_{0}$ space is neither $\mu^{*}$$R_{0}$ nor $\mu$$R_{0}$. Further, conditions under which the $(\mu X, \mu Y)$continuous image of $\mu^{*}$$R_{0}$ space becomes $\mu^{*}$$R_{0}$ and $\mu$$R_{0}$ are established. Also, some new versions of separation axioms are defined and they are used as a tool to investigate $\mu^{*}$$R_{0}$ and $\mu^{*}$$R_{1}$ spaces. Further, the conditions under which these spaces coincide are obtained.Keywords: Μ∗Open(Closed) Map, Μ∗Kernel, Μ∗T0, Μ∗T1, Μ∗T2 Spaces

Pages 431440In this paper we introduce the class of grand Lebesgue spaces associated to a Banach function space $X$ by replacing the role of the $L^1$norm by the norm $\\cdot\_X$ in the classical construction of the generalized grand Lebesgue spaces. Also, we study the inclusion property of these spaces.Keywords: Grand Lebesgue Spaces, Banach Function Spaces, Inclusion, Young Function, Orlicz Spaces

Pages 441459
This paper deals with the existence and multiplicity of nonnegative generalized solutions for a class of secondorder Kirchhofftype problems. It is important to mention that no asymptotic condition is required in the nonlinear term either at zero or at infinity. Our approach is based on the variational methods and critical point theory.
Keywords: Generalized Solution, SecondOrder KirchhoffType Equation, Critical Point Theory, Variational Methods 
Pages 461491It is observed from the surveyed literature that there is no sufficient study of quasiweakly contractive operators in the context of $b$metriclike spaces. From this background information, this paper introduces a new unified notion of the quasiweakly contractive operator in $b$metriclike space. It examines the existence and uniqueness of invariant points of such operators. The idea put forward herewith subsumes a few known results in the literature. Nontrivial illustrations are constructed to verify our proposed concepts and to compare them with other corresponding ones. Corollaries which reduce our findings to other famous ideas are presented and discussed. As an application, one of our obtained corollaries is utilised to investigate new existence criteria for solving a class of boundary value problem.Keywords: Fixed Point, $B$MetricLike, Integral Equation