Some New Observations and Results for Convex Contractions of Istratescu’s Type (original) (raw)

On Istrăţescu Type Contractions in b-Metric Spaces

Mathematics

In this paper, we introduce the notions of α -almost Istrăt̨escu contraction of type E and of type E ∗ in the setting of b-metric space. The existence of fixed points for such mappings is investigated and some examples to illustrate the validity of the main results are considered. In the last part of the paper, we list some immediate consequences.

Fixed Point Results for Cirić and Almost Contractions in Convex b-Metric Spaces

Mathematics, 2022

We establish a fixed point theorem for Cirić contraction in the context of convex b-metric spaces. Furthermore, we ensure that there is a fixed point for the maps satisfying the condition (B) (a kind of almost contraction ) in convex b-metric spaces and demonstrate its uniqueness as well. Supporting examples to substantiate the generality of the proved results are given.

Fixed Point of Almost Contraction in b -Metric Spaces

Journal of Mathematics, 2020

In this paper, we introduce a generalized multivalued ( α , L)-almost contraction in the b -metric space. Furthermore, we prove the existence and uniqueness of the fixed point for a specific mapping. The result presented in this paper extends some of the earlier results in the existing literature. Moreover, some examples are given to illuminate the usability of the obtained results.

On Convex F-Contraction in b-Metric Spaces

Axioms, 2021

In this paper, we introduce a notion of convex F-contraction and establish some fixed point results for such contractions in b-metric spaces. Moreover, we give a supportive example to show that our convex F-contraction is quite different from the F-contraction used in the existing literature since our convex F-contraction does not necessarily contain the continuous mapping but the F-contraction contains such mapping. In addition, via some facts, we claim that our results indeed generalize and improve some previous results in the literature.

New fixed point theorems for set-valued contractions in b-metric spaces

Journal of Fixed Point Theory and Applications, 2017

In this paper we indicate a way to generalize a series of fixed point results in the framework of b-metric spaces and we exemplify it by extending Nadler's contraction principle for set-valued functions (see Multi-valued contraction mappings, Pac. J. Math., 30 (1969), 475-488) and a fixed point theorem for set-valued quasi-contractions functions due to H.

EXISTENCE AND UNIQUENESS OF FIXED POINT FOR NEW CONTRACTIONS IN RECTANGULAR b-METRIC SPACES

South East Asian J. of Mathematics and Mathematical Sciences

In this article, we give some new examples of rectangular b-metric spaces which are neither rectangular metric space nor metric space. After that we prove existence and uniqueness of new fixed points for some new contractions in rectangular b-metric spaces. Then we validate these results with suitable, appro- priate and innovative examples.

New fixed point theorems for (ϕ,F)−(ϕ, F)-(ϕ,F)−contraction on rectangular b-metric spaces

2022

The Banach contraction principle is the most celebrated fixed point theorem, it has been generalized in various directions. In this paper, inspired by the concept of (ϕ,F)−(ϕ, F)-(ϕ,F)−contraction in metric spaces, introduced by Wardowski. We present the notion of (ϕ,F)−(ϕ, F)-(ϕ,F)−contraction in b−b-b−rectangular metric spaces to study the existence and uniqueness of fixed point for the mappings in this spaces. Our results improve many existing results.

Review of the convex contractions of Istratescu's type in various generalized metric spaces

Advances in the Theory of Nonlinear Analysis and its Application, 2020

The main purpose of this paper is to consider convex contraction of Istratescu’s type in various generalized metric spaces (partial metric spaces, cone metric spaces, cone b-metric spaces, partial b-metric spaces, and others). In it, among other things, we generalize, extend, correct and enrich the recent announced results in existing literature.