1,383 Results Found

This paper surveys some recent simple proofs of various fixed point and existence theorems for continuous mappings in ${\mathbb{R}}^n$...

In the present paper, we propose a common fixed point theorem for three commuting mappings via a new contractive condition which generalizes fixed point theorems of Darbo, Hajji and Aghajani et al. An application is also given to illustrate our main...

The paper suggests a general method for proving the fact whether a certain set is p-computable or not. The method is based on a polynomial analogue of the classical Gandy’s fixed point theorem. Classical Gandy’s theorem deals with the extension of a...

The goal of this paper is to consider a differential equation system written as an interesting equivalent form that has not been used before. Using Perov’s fixed point theorem in generalized metric spaces, the existence and uniqueness of the so...

The authors explore fixed-point theory in b-metric spaces and strong b-metric spaces. They wish to prove some new extensions of the Covitz and Nadler fixed-point theorem in b-metric spaces. In so doing, they wish to answer a question proposed by Kirk...

We define sequential completeness for ⊤-quasi-uniform spaces using Cauchy pair ⊤-sequences. We show that completeness implies sequential completeness and that for ⊤-uniform spaces with countable ⊤-uniform bases, completeness a...

In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point theorem in Ba...

In the present article, the Schauder-type fixed point theorem for the class of fuzzy continuous, as well as fuzzy compact operators is established in a fuzzy normed linear space (fnls) whose underlying t-norm is left-continuous at $(1,1)$. In the fuzzy...

In this paper, we prove a new fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U, which generalizes Nadler’s fixed point theorem. We also establish some fi...

In this work, a functional variant of the polynomial analogue of Gandy’s fixed point theorem is obtained. Sufficient conditions have been found to ensure that the complexity of recursive functions does not exceed polynomial bounds. This opens u...

In this article, we introduce several new extensions of Darbo’s fixed point theorem with newly constructed contraction functions associated with the measure of noncompactness. We apply our new extensions to prove the existence of solutions for...

The purpose of this article is to establish the solvability of the 2-Dimensional dissipative cubic nonlinear Klein-Gordon equation (2DDCNLKGE) through periodic boundary value conditions (PBVCs). The analysis of this study is founded on the Galerkin&r...

Integral equations, which are defined as “the equation containing an unknown function under the integral sign”, have many applications of real-world problems. The second type of Fredholm integral equations is generally used in radiation t...

This work explores the existence and uniqueness criteria for the solution of hybrid Caputo–Hadamard fractional sequential differential equations (HCHFSDEs) by employing Darbo’s fixed-point theorem. Fractional differential equations play a...

In this work, the existence and uniqueness of solutions to a sequential fractional (Hybrid) differential equation with hybrid boundary conditions were investigated by the generalization of Dhage’s fixed point theorem and Banach contraction mapp...

In this paper, we first establish a new fixed point theorem that generalizes and unifies a number of well-known fixed point results, including the Banach contraction principle, Kannan’s fixed point theorem, Chatterjea fixed point theorem, Du-Rassias...

We establish the existence of positive solutions for systems of second–order differential equations with discontinuous nonlinear terms. To this aim, we give a multivalued vector version of Krasnosel’skiĭ’s fixed point theorem in con...

In this theory, the existence of a mild solution for a neutral partial integrodifferential nonlocal system with finite delay is presented and proved using the techniques of the Monch–Krasnosel’skii type of fixed point theorem, a measure o...

In this paper, we state and establish a new fixed point theorem for generalized Ćirić-type contraction in Kaleva-Seikkala’s type fuzzy b-metric space. Our results improve and extend some well-known results in the literature. Some exam...

In this paper, we investigate new fixed point theorems for generalized Meir–Keeler type nonlinear mappings satisfying the condition (DH). As applications, we obtain many new fixed point theorems which generalize and improve several results avai...

In this paper, we present some new generalizations of Mizoguchi-Takahashi’s fixed point theorem which also improve and extend Du-Hung’s fixed point theorem. Some new examples illustrating our results are also given. By applying our new results, some...

No previous study has involved uncertain fractional differential equation (FDE, for short) with jump. In this paper, we propose the uncertain FDEs with jump, which is driven by both an uncertain V-jump process and an uncertain canonical process. Firs...

In this paper, by applying the abstract maximal element principle of Lin and Du, we present some new existence theorems related with critical point theorem, maximal element theorem, generalized Ekeland’s variational principle and common (fuzzy) fixed...

In this paper, we introduce the notion of quadratic quasicontractive mapping and prove two generalizations of some classical fixed point theorems. Furthermore, we present some examples to support our main results.

This paper establishes new fixed-point theorems in the framework of complete p-normed spaces, where $p\in (0,1]$. By extending the classical Banach, Schauder, and Krasnosel’skii fixed-point theorems, we derive several results for the sum of con...

An overview of fixed-point theorems (F.P.T.s) for multifunctions in probabilistic metric spaces is given. Extensions of the fixed-point theorems on probabilistic metric spaces of Nadler, Hadžić, Itoh, and Miheţ are presented. In the en...

We introduce a new hybrid contraction condition in the setting of G-metric spaces that unifies Banach-, Kannan-, and Chatterjea-type contractions applied to an iterate $T^p$ of a self-map T. Under a natural coefficient constraint, we prove that such a m...

This paper is devoted to studying the existence and uniqueness of a system of coupled fractional differential equations involving a Riemann–Liouville derivative in the Cartesian product of fractional Sobolev spaces $\mathcal{E}=W_{a^{+}}^{{\gamma }_1,1}(a,b)\times W_{a^{+}}^{{\gamma }_2,1}(a,b)$. Our st...

We solve a question posed by E. Karapinar, F. Khojasteh and Z.D. Mitrović in their paper “A Proposal for Revisiting Banach and Caristi Type Theorems in b-Metric Spaces”. We also characterize the completeness of b-metric spaces with t...

In this paper, we prove some fixed point theorems for the nonlinear operator $A·B+C$ in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the appl...

In this paper, we introduce the concept of cone metric space over a topological left module and we establish some coincidence and common fixed point theorems for self-mappings satisfying a condition of Lipschitz type. The main results of this paper p...

The paper aims to generalize several known Darbo- and Sadovskii-type fixed point theorems. These generalizations weaken the assumptions used so far. In addition, an example of an application is presented.

In this manuscript, we utilize the concept of modified $\omega$ -distance mapping, which was introduced by Alegre and Marin [Alegre, C.; Marin, J. Modified $\omega$ -distance on quasi metric spaces and fixed point theorems on complete quasi m...

The aim of this paper is to provide new ways of dealing with dynamic programming using a context of newly proven results about fixed-point problems in linear spaces endowed with a fuzzy norm. In our paper, the general framework is set to fuzzy normed...

Our paper is devoted to the issue of the existence and uniqueness of common fixed points for two mappings in complete b-metric spaces by virtue of the new functions F and $\theta$, respectively. Moreover, two specific examples to indicate the validity...

In the present paper, our main work aims to discover the existence result of the fractional order non-linear Hadamard functional integral equations on $[1,a]$ by employing the theory of measure of non-compactness together with the fixed point theory in...

In this paper, we prove some Banach fixed point theorems in generalized metric space where the contractive conditions are endowed with the Hadamard product of real symmetric positive definite matrices. Since the condition that a matrix A converges to...

In this paper, we introduce the concepts of an inferior idempotent cone and a $\mathbb{BID}$-cone b-metric space over Banach algebra. We establish some new existence theorems and fixed point theorems in the setting of complete $\mathbb{BID}$-cone b-metric spaces over Bana...

In this paper, we introduce the concept of $\mathcal{R}$-nonexpansive self-mappings defined on a suitable subset K of a Banach space, wherein $\mathcal{R}$ stands for a transitive binary relation on K, and utilize the same to prove a relation-theoretic variant of classical...

We present the notion of orthogonal $\mathcal{F}$ -metric spaces and prove some fixed and periodic point theorems for orthogonal ${\perp }_{\mathsf{\Omega }}$ -contraction. We give a nontrivial example to prove the validity of our result. Finally, as application, w...

In this paper, we establish a fixed-point theorem for mixed monotone operators in ordered Banach algebras by introducing a novel contraction condition formulated in terms of the product law, which represents a significant departure from the tradition...

Sets, probability, and neutrosophic logic are all topics covered by neutrosophy. Moreover, the classical set, fuzzy set, and intuitionistic fuzzy set are generalized using the neutrosophic set. A neutrosophic set is a mathematical concept used to sol...

We obtain quasi-metric versions of the famous Meir–Keeler fixed point theorem from which we deduce quasi-metric generalizations of Boyd–Wong’s fixed point theorem. In fact, one of these generalizations provides a solution for a ques...

Our paper is devoted to indicating a way of generalizing Mann’s iteration algorithm and a series of fixed point results in the framework of b-metric spaces. First, the concept of a convex b-metric space by means of a convex structure is introdu...

In this paper, we consider a common fixed-point theorem with a contractive iterative at a point in the setting of complete dislocated b-metric space that was initiated by Seghal. We shall consider an example and application in fractional differential...

We define the class of extended $b_v\left(s\right)$-metric spaces by replacing the real number $s\ge 1$ with a strictly increasing continuous function $\varphi$ in the definition of a $b_v\left(s\right)$-metric space. Also, we presented an example for this newly introduced space and...

In this paper, we prove a Sehgal–Guseman-type fixed point theorem in b-rectangular metric spaces which provides a complete solution to an open problem raised by Zoran D. Mitrović (A note on a Banach’s fixed point theorem in b-rectang...

In this paper, we extend Darbo’s fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main...

In the present paper, we provide and verify several results obtained by using the Chatterjea and $\stackrel{`}{\mathrm{C}}$iri$\stackrel{`}{\mathrm{c}}$ fixed-point theorems by using $(\alpha -\psi )$-contractive mapping in $C^{*}$-algebra-valued metric space. We provide some examples and an applic...

Over the years, the concept of metric space has been extended in several directions, and numerous common fixed point theorems for multivalued mappings in complete metric space have been demonstrated. In this paper, we prove a general fixed point theo...