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We obtain sufficient conditions for weighted integrability of a generalized Fourier–Bessel transform of functions from generalized integral Lipschitz classes. These conditions are analogues of the well-known Móricz conditions for classical Fourier transform. In addition, a Boas type result associating the behavior of a function and the smoothness of its generalized Fourier–Bessel transform is proved. [ABSTRACT FROM AUTHOR]

This research investigated different types of convex contractions in the setting of extended b-metric spaces from the point of view of the existence and uniqueness of their fixed points. The assumptions imposed on involved mappings refer to convexity of order 2, two-sided convexity or Ćirić-type convexity, which also fulfill a continuity type condition. An example was provided to emphasize the usability of the results. [ABSTRACT FROM AUTHOR]

This research investigated different types of convex contractions in the setting of extended $ b $-metric spaces from the point of view of the existence and uniqueness of their fixed points. The assumptions imposed on involved mappings refer to convexity of order $ 2 $, two-sided convexity or Ćirić-type convexity, which also fulfill a continuity type condition. An example was provided to emphasize the usability of the results.

In this paper, the concepts of Wardowski-type set-valued contractions and Işik-type set-valued contractions are introduced and fixed point theorems for such contractions are established. A positive answer to the open Question is given. Examples to support main theorems and an application to integral inclusion are given. [ABSTRACT FROM AUTHOR]

The purpose of this article is to obtain common fixed point results in b-metric spaces for generalized rational contractions involving control functions of two variables. We provide an example to show the originality of our main result. As outcomes of our results, we derive certain fixed and common fixed point results for rational contractions presuming control functions of one variable and constants. As an application, we investigate the solution of an integral equation.

In this research article, we give the notion of graphic F-contraction in the setting of F-metric space and establish some fixed point results. We also supply some examples to demonstrate the brilliance of the established results. We also establish some fixed point results for orbitally continuous and orbitally G -continuous graphic F-contractions as applications of our main results. Also, we discuss the existence and the uniqueness of solutions of functional equations involving in dynamic programming.

Ordinary differential equations that includes stochastic processes in their vector fields are called random ordinary differential equations, that are considered through this work as a Weiner process or also called Brownian motion. In this paper, fuzzy random ordinary differential equations are considered, in which the fuzziness appears in the initial conditions in terms of triangular fuzzy numbers. Such equations are crucial in the theory of random dynamical systems and/or modern control theory and therefore the existence of a unique solution of such equations is of great importance. The statement and the proof of the existence and uniqueness theorem of fuzzy random ordinary differential equations is the main objective of this paper, which is proved using Banach contraction mapping theorem. [ABSTRACT FROM AUTHOR]

The aim of this research article is to obtain fixed point results in the context of F -bipolar metric spaces. The obtained results extend some fixed point theorems in the existing literature. We also provide a non-trivial example to validate our claims. The existence and uniqueness of the solution of the integral equation are proved as applications of our leading results. Furthermore, the existence of the unique solution in homotopy theory is also investigated. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two-person zero-sum differential game with incomplete information on the initial state, namely, the first player has a private information while the second player knows only a probability distribution on the initial state, and obtain the existence of its value functions. The main novelty lies in the method for which we apply a generalized weak contraction for dynamic systems and terminal cost functions instead of the Lipschitz contractive condition on a partially ordered metric space. [ABSTRACT FROM AUTHOR]

In this research article, we give the notion of graphic F-contraction in the setting of F - metric space and establish some fixed point results. We also supply some examples to demonstrate the brilliance of the established results. We also establish some fixed point results for orbitally continuous and orbitally G-continuous graphic F-contractions as applications of our main results. Also, we discuss the existence and the uniqueness of solutions of functional equations involving in dynamic programming. [ABSTRACT FROM AUTHOR]

The purpose of this article is to obtain common fixed point results in b-metric spaces for generalized rational contractions involving control functions of two variables. We provide an example to show the originality of our main result. As outcomes of our results, we derive certain fixed and common fixed point results for rational contractions presuming control functions of one variable and constants. As an application, we investigate the solution of an integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we aim to obtain some new common attractors with the assistance of finite families of generalized contractive mappings, that belong to the special class of mappings defined on a partial metric space. Consequently, a variety of results for iterated function systems satisfying a different set of generalized contractive conditions are acquired. We present some examples to reinforce the results proved herein. These results generalize, unify and extend a variety of results that exist in current literature.

In this research paper, we concentrate on the existence and uniqueness of common fixed points of various mappings in b 2 metric space under generalized (ϕ , f) λ -expansive conditions and implicit contractive conditions. Additionally, we derive a progression of noteworthy approaches and ideas extending the conclusions on the real metric space to the b 2 metric space, which advances the investigation of the b 2 metric space will be able to advance. [ABSTRACT FROM AUTHOR]

This paper introduces a complete G n -Menger space and defines the Hausdorff–Pompeiu distance in the space. Furthermore, we show a novel fixed-point theorem for G n -Menger- θ -contractions in fractal spaces. [ABSTRACT FROM AUTHOR]

One recent and prolific direction in the development of fixed point theory is to consider an operator T : X → X defined on a metric space (X , d) which is an F—contraction, i.e., T verifies a condition of type τ + F (d (T (x) , T (y)) ≤ F (d (x , y)) , for all x , y ∈ X , T (x) ≠ T (y) , where τ > 0 and F : (0 , ∞) → R satisfies some suitable conditions which ensure the existence and uniqueness for the fixed point of operator T. Moreover, the notion of F-contraction over a metric space (X , d) was generalized by considering the notion of (G , H) —contraction, i.e., a condition of type G (d (T x , T y)) ≤ H (d (x , y)) , for all x , y ∈ X , T x ≠ T y for some appropriate G , H : (0 , ∞) → R functions. Recently, the abovementioned F-contraction theory was extended to the setup of cone metric space over the topological left modules. The principal objective of this paper is to introduce the concept of vectorial dislocated metric space over a topological left module and the notion of A-Cauchy sequence, as a generalization of the classical Cauchy sequence concept. Furthermore, based on the introduced concept, a fixed point result is provided for an operator T : X → X , which satisfies the condition (G , H) —contraction, where G , H are defined on the interior of a solid cone. [ABSTRACT FROM AUTHOR]

In this paper, we aim to obtain some new common attractors with the assistance of finite families of generalized contractive mappings, that belong to the special class of mappings defined on a partial metric space. Consequently, a variety of results for iterated function systems satisfying a different set of generalized contractive conditions are acquired. We present some examples to reinforce the results proved herein. These results generalize, unify and extend a variety of results that exist in current literature. [ABSTRACT FROM AUTHOR]

In this paper, we use a new technique for the treatment of systems based on the advantage of vector-valued norms and of the weak topology. We first present vector versions of the Leray-Schauder alternative and then some Krasnoselskii type fixed point theorems for a sum of two mappings. Applications are given to a system of nonlinear transport equations, and systems of mixed fractional differential equations. [ABSTRACT FROM AUTHOR]

The notion of a -generalized-search multivalued functional on an -quasimetric space is introduced. An existence theorem for zeros of such functionals is proved. As corollaries, theorems on coincidence and fixed points of multivalued mappings of -quasimetric spaces are proved. In particular, Nadler's well-known theorem on fixed points of multivalued contraction mappings is generalized to the case of an -quasimetric space. For a large class of single-valued mappings, including generalized contractions, a theorem on the existence of a (not necessarily unique) fixed point is proved. This theorem extends the existence part of E. S. Zhukovskii's recent fixed-point theorem for generalized contractions, which is a generalization to -quasimetric spaces of Krasnosel'skii's well-known fixed-point theorem and Browder's fixed-point theorem (equivalent to Krasnosel'skii's theorem). [ABSTRACT FROM AUTHOR]

Let (X , ·) be a Hilbert space and T : X → X be a decreasing operator. Under a metric condition involving the convex combination of x and T(x), we will prove some fixed point theorems which generalize and complement several results in the theory of nonlinear operators. Our results are closely related to the admissible perturbations approach in fixed point theory. [ABSTRACT FROM AUTHOR]

Let (X1,→) and (X2, ↬) be two L-spaces, U be a nonempty subset of X1 × X2 such that UX1:= {X2 ∈ X2 | (X1, X2) ∈ U} is nonempty, for each X1 ∈ X1. Let T1: X1 → X1, T2: U → X2 be two operators and T: U → X1 × X2 defined by T(X1,X2):= (T1(X1),T2(X1,X2)). If we suppose that T(U) ⊂ U, FT1 ≠ ∅ and FT2(X1,·) ≠ ∅ for each X1 ∈ X1, the problem is in which additional conditions T is a weakly Picard operator? In this paper we study this problem in the case when the convergence structures on X1 and X2 are defined by metrics. Some applications to the fixed point equations on spaces of continuous functions are also given. [ABSTRACT FROM AUTHOR]

In this article, the concept of cyclic weakly generalized contraction mapping of Ciric type has been introduced and the existence of a fixed point for such mappings in the setup of complete metric spaces has been established. Result obtained extends and improves some fixed point results in the literature. Example is also given to show that class of contraction mappings introduced in the paper is strictly larger class than the class of mappings used in the literature and thus ensures wider applicability of the result by producing the solutions to new problems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems. [ABSTRACT FROM AUTHOR]

In this paper, we have achieved fixed point results for pair of fuzzy mappings satisfying Ciric type contraction on a sequence contained in an open ball in ordered left (right) K-sequentially complete dislocated quasi metric space. An example and an application are presented to demonstrate the novelty of the results. Our results generalize and extend some recent results in literature. [ABSTRACT FROM AUTHOR]

We obtain a contractive condition for the existence and uniqueness of fixed points for a generalized contraction-type mapping. The present study focuses on providing a method for the existence of fixed points for nonlinear mappings. Sufficient conditions for the existence and uniqueness of such points are obtained using Ishikawa iteration process. Moreover, an example is given. [ABSTRACT FROM AUTHOR]

The recent articles of Arutyunov and Greshnov extend the Banach and Hadler Fixed-Point Theorems and the Arutyunov Coincidence-Point Theorem to the mappings of (q1, q2)-quasimetric spaces. This article addresses similar questions for f-quasimetric spaces.Given a function f: R +2 → R+ with f(r1, r2) → 0 as (r1, r2) → (0, 0), an f-quasimetric space is a nonempty set X with a possibly asymmetric distance function ρ: X2 → R+ satisfying the f-triangle inequality: ρ(x, z) ≤ f(ρ(x, y), ρ(y, z)) for x, y, z ∈ X. We extend the Banach Contraction Mapping Principle, as well as Krasnoselskii's and Browder's Theorems on generalized contractions, to mappings of f-quasimetric spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to extend Krasnoselskii’s fixed point theorem to the case of generalized Banach spaces for multivalued operators. As application, we will give an existence result for a system of Fredholm-Volterra type differential inclusions.

In this paper, we present the concept of Θ − ( σ , ξ ) Ω -contraction mappings and we nominate some related fixed point results in ordered p-metric spaces. Our results extend several famous ones in the literature. Some examples and an application are given in order to validate our results.

The paper contains some fixed point theorems for generalized contractions in dislocated quasi-metric spaces. The simplest requirement is condition: p(f(y), f(x)) ≤ g(p(y, x)), for all x, y ∈ X, where p is a dislocated quasi-metric on X (if p(x, y) = p(y, x) = 0, then x = y; 0 ≤ p(x, z) ≤ p(x, y) + p(y, z)) and g is a comparison function of a general type. Our results are far extensions of some known fixed point theorems for dislocated quasi-metric spaces. [ABSTRACT FROM AUTHOR]

In the present article, we study some fixed point theorems for a hybrid class of generalized contractive operators in the context of b-rectangular metric spaces. Examples justifying theorems and an open problem regarding to further generalizations for this type of operators are also given. [ABSTRACT FROM AUTHOR]

In this paper we will point out an error in proving some results on finite iterated function systems consisting of Kannan maps, Reich maps and Chatterjea type maps. In this respect, some counter-examples are given. We also answer some open questions on iterated function systems consisting of contractive maps of Reich type and we present revisions of some theorems on iterated function systems consisting of Kannan, Reich and Chatterjea type maps, by adding a commutativity assumption on the maps. [ABSTRACT FROM AUTHOR]

In this manuscript, using generalized type contraction, multi-valued coupled fixed point results in the set up of partially ordered metric space are studied. For the validity of the derived result appropriate example and application are also provided. [ABSTRACT FROM AUTHOR]

It is shown that a series of recent (2012-2016) generalizations of the notion of contraction ( F-contraction, weak F-contraction, etc.) in fact reduce to known notions of contraction (due to Browder, Boyd and Wong, Meir and Keeler, etc.). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concept of the homeomorphism metric space and to prove the fixed point theorems and the best proximity point theorems for generalized contractions in such spaces. The multiplicative metric space is a special form of the homeomorphism metric space. The results of this paper improve and extend the previously known ones in the literature. [ABSTRACT FROM AUTHOR]

The notion of generalized contractions of rational type on a closed ball is introduced and used to establish some common fixed point theorems for two, three and four mappings in complete ordered partial metric spaces. These results improve several well-known, primary and conventional results. We give an example to illustrate the main idea of our results that there are mappings which have only fixed points inside or on the closed ball instead of whole space. [ABSTRACT FROM AUTHOR]

In this manuscript, we construct three viscosity implicit iteration schemes based on generalized contractions for strictly pseudo-contractive mappings. The first scheme is used to approximate a fixed point of a single strictly pseudo-contractive mapping, the second scheme is used to approximate a common fixed point of a finite family of strictly pseudo-contractive mappings, the third scheme is used to approximate a common fixed point of a countable family of strictly pseudo-contractive mappings. Furthermore, three strong convergence theorems based on the purposed iterative schemes are established in the framework of Banach spaces. Finally, three numerical examples are also given to show the efficiency and implementation of our schemes. The main results of this paper modify and improve many important recent results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to extend Krasnoselskii's fixed point theorem to the case of generalized Banach spaces for singlevalued and multivalued operators. As applications, we will give some existence results for abstract system of Fredholm-Volterra type differential equations and inclusions.

We obtain extensions of Matkowski's fixed point theorem for generalized contractions of Ciric's type on 0-complete partial metric spaces and on ordered 0-complete partial metric spaces, respectively.

In the paper general theorems on common fixed point for four mappings are presented. The results are compact and they extend and unify the respective part of the fixed point theory. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the generalized viscosity implicit rules of one nonexpansive mapping in uniformly smooth Banach spaces. Strong convergence theorems of the rules are proved under certain assumptions imposed on the parameters. As applications, we use our main results to solve fixed point problems of strict pseudocontractions in Hilbert spaces and variational inequality problems in Hilbert spaces. Finally, we also give one numerical example to support our main results. [ABSTRACT FROM AUTHOR]

Boyd and Wong in their celebrated paper 'On nonlinear contractions' assumed the comparison function to be upper semicontinuous from the right. Our requirement presented in this paper is much more general and it extends also the well-known Matkowski condition. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of modified w -distance ( mw -distance) on a quasi-metric space which generalizes the concept of quasi-metric. We obtain a fixed point theorem for generalized contractions with respect to mw -distances on complete quasi-metric spaces. [ABSTRACT FROM AUTHOR]