Sahand Communications in Mathematical Analysis
Volume:21 Issue: 1, Winter 2024

The paper aims to introduce and study an algebra of asymptotically almost periodic generalized ultradistributions. These generalized ultradistributions contain  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.

In this paper, we have proved and stated the Sitaru-Schweitzer type inequality for fuzzy integrals and  also we state this inequality for pseudo-integrals in two classes. The first one is for  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.

In this article, we define  generalized $(\varphi,\sigma,\gamma)$-rational contraction, generalized $(\alpha\beta,\varphi\theta,F)$-rational  contraction  and establish some new fixed  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.

In this study, the quaternion Hankel transform is developed. Basic operational properties and inversion formula of quaternion Hankel transform are derived. Parseval’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’s problem.

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   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.

In this paper, we introduce the notion of the ternary generalized Jordan ring homomorphism on ternary non-Archimedean Banach algebras. Utilizing  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.

In this paper, we aim to  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 Hölder'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.

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  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  defined, along with some illustrative examples.

The generalized $M$-series is a hybrid function of generalized Mittag-Leffler function and generalized hypergeometric function.  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  our main findings in Hadamard product of two known functions.

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,  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.

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.

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 $k$.

In this paper, we are interested in studying an integro-differential equation with two-point integral boundary conditions using  the Caputo fractional derivative of order $2< \varrho \leq 3$. 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.

This article  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.

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  the set of common fixed points of a countable family of nonexpansive mappings.

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.

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.

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.

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.

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  some basic properties of their structure will be obtained. Some characterizations of  the basis of fuzzy generalized topology, fuzzy generalized cotopology and the product of fuzzy generalized topological spaces will also be shown.