Existence, uniqueness, Ulam–Hyers–Rassias stability, well-posedness and data dependence property related to a fixed point problem in gamma-complete metric spaces with application to integral equations

In this paper, we study a fixed point problem for certain rational contractions on γ-complete metric spaces. Uniqueness of the fixed point is obtained under additional conditions. The Ulam–Hyers–Rassias stability of the problem is investigated. Well-posedness of the problem and the data dependence property are also explored. There are several corollaries of the main result. Finally, our fixed point theorem is applied to solve a problem of integral equation. There is no continuity assumption on the mapping.

New Results on F-Contractions in Complete Metric Spaces

The main purpose of this paper is to improve, generalize, unify, extend and enrich the recent results established by Dung and Hang (2015), Piri and Kumam (2014, 2016), and Singh et al. (2018). In our proofs, we only use the property (F1) of Wardowski’s F-contraction, while the many authors in their papers still use all tree properties of F-contraction as well as two new properties introduced by Piri and Kumam. Our approach in this paper indicates that for most results with F-contraction, property (F1) is sufficient. It is interesting to investigate whether (F1) is sufficient in the case of multi-valued mappings.

Investigating Distributional Chaos for Operators on Fréchet Spaces

In this paper, various notions of chaos for continuous linear operators on Fréchet spaces are investigated. It is shown that an operator is Li–Yorke chaotic if and only if it is mean Li–Yorke chaotic in a sequence whose upper density equals one; that an operator is mean Li–Yorke chaotic if and only if it admits a mean Li–Yorke pair, if and only if it is distributionally chaotic of type 2, if and only if it has an absolutely mean irregular vector. As a consequence, mean Li–Yorke chaos is not conjugacy invariant for continuous self-maps acting on complete metric spaces. Moreover, the existence of invariant scrambled sets (with respect to certain Furstenberg families) of a class of weighted shift operators is proved.

Some fixed point results of F-Contraction mapping in D-metric spaces by Samet’s method

The aim of this paper is to study the F-contraction mapping introduced by Wardowski to obtain fixed point results by method of Samet in generalized complete metric spaces. Our findings extend the results announced by Samet methods and some other works in generalized metric spaces.

Wardowski’s Contraction and Fixed Point Technique for Solving Systems of Functional and Integral Equations

In this manuscript, some tripled fixed point results are presented in the framework of complete metric spaces. Furthermore, Wardowski’s contraction was mainly applied to discuss some theoretical results with and without a directed graph under suitable assertions. Moreover, some consequences and supportive examples are derived to strengthen the main results. In the last part of the paper, the obtained theoretical results are used to find a unique solution to a system of functional and integral equations.

Some fixed point theorems on equivalent metric spaces

This paper aims to analyze the existence of fixed points for mappings defined on complete metric spaces satisfying almost contractive conditions and a general contractive inequality of integral type. The existence of a fixed point is ensured by hypotheses formulated in terms of equivalent metric spaces.

Contractive Mappings on Metric Spaces with Graphs

We establish fixed point, stability and genericity theorems for strict contractions on complete metric spaces with graphs.

Fixed Points and Stability for Integral-Type Multivalued Contractive Mappings

The existence and iterative approximations of fixed points concerning two classes of integral-type multivalued contractive mappings in complete metric spaces are proved, and the stability of fixed point sets relative to these multivalued contractive mappings is established. The results obtained in this article generalize and improve some known results in the literature. An illustrative example is given.

A Fixed Point Technique for Solving an Integro-Differential Equation Using Mixed-Monotone Mappings

The objective of this manuscript is to present new tripled fixed point results for mixed-monotone mappings by a pivotal lemma in the setting of partially ordered complete metric spaces. Our outcomes sum up, enrich, and generalize several results in the current writing. Moreover, some examples have been discussed to strengthen and support our theoretical results. Finally, the theoretical results are applied to study the existence and uniqueness of the solution to an integro-differential equation.

Solving a Nonlinear Fredholm Integral Equation via an Orthogonal Metric

In this paper, we prove fixed point theorems using orthogonal triangular α -admissibility on orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by the obtained results. An instance to help our outcome is being presented.