Related papers: New fixed point theorems for $(\phi, F)-$contracti…

In this paper, we give and prove two Chatterjea type fixed point theorems on partial $b$-metric space. We propose an extension to the Banach contraction principle on partial $b$-metric space which was already presented by Shukla and also…

In this paper, we present the Brouwer-Schauder-Tychonoff fixed point theorem on locally convex spaces as the following extension and improvement: Suppose that S is a compact star-shaped subset with respect to p in S with its convexity index…

In the present paper, we prove generalizations of Banach, Kannan, Chatterjea, \'Ciri\'c-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mappings contracting perimeters of triangles. We consider corresponding…

In this paper, we investigate the existence and uniqueness of fixed point for partially ordered contraction type operators in Banach Space. We also present applications to integral and differential equations.

Fixed point theory studies conditions under which nonexpansive maps on Banach spaces have fixed points. This paper examines the open question of whether every reflexive Banach space has the fixed point property. After surveying classical…

Very recently, Berinde and P\u{a}curar obtained in [V. Berinde and M. P\u{a}curar, Approximating fixed points of enriched contractions in Banach spaces. Journal of Fixed Point Theory and Applications. \textbf{22}(2) (2020), 1--10.] an…

We focus on the new type perturbed metric spaces and introduce a contraction mapping namely new type perturbed Kannan mappings. For these mappings, we show that Banach's fixed point theorem holds. Moreover, this new generalization of…

Based on the idea of randomizing the traditional space theory of functional analysis, random functional analysis has been developed as functional analysis over random metric spaces, random normed modules and random locally convex modules.…

Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.

In this article, utilizing the concept of w-distance, we prove the celebrated Banach's fixed point theorem in metric spaces equipped with an arbitrary binary relation. Necessarily our findings unveil another direction of relation-theoretic…

There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…

The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…

In this article, we introduce the LR-$(\delta,\phi)$ quasi partial $b$-metric space. Also, the common fixed point theorem on complete LR-$(\delta,\phi)$ quasi partial $b$-metric space has been proved. A non-trivial example is also given.

While numerous extensions of Banach's fixed point theorem typically offer only sufficient conditions for the existence and uniqueness of a fixed point and the convergence of iterative sequences, this study introduces a generalization…

Some fixed point results of classical theory, such as Banach's Fixed Point Theorem, have been previously extended by other authors to asymmetric spaces in recent years. The aim of this paper is to extend to asymmetric spaces some others…

This paper advances a line of research in fixed point theory initiated by M. Bessenyei and Z. P\'ales, building on their introduction of the triangle function concept in [J. Nonlinear Convex Anal, Vol 18 (3), 515-524 (2017)]. By applying…

In this paper, we show the new fixed point theorem in metric spaces. Furthermore, for this fixed point theorem, we apply to the Collatz conjecture.

We derive two fixed point theorems for a class of metric spaces that includes all Banach spaces and all complete Busemann spaces. We obtain our results by the use of a 1-Lipschitz barycenter construction and an existence result for…

In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…

In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed…