The main goal of this work is to present GF -metric space, a new generalization of G-metric space. A comparison between the classes of G-metric spaces, GP-metric spaces, Gb-metric spaces, generalized ...Gb-metric spaces, and G∗ -metric spaces and the class of GF - metric spaces is also presented. We examine a few fundamental aspects of this newly defined abstract space. Proving the Banach contraction principle and the fixed point result for (ψ, ϕ)-contractive mapping in the context of GF -metric spaces is the paper’s secondary goal
This manuscript proves the existence of a single common fixed point of two joint A,B generalized cyclic ϕ−abc weak nonexpansive mappings, where A and B are compact sets. The result in particular ...demonstrated a single fixed point of generalized cyclic ϕ−abc weak nonexpansive mappings, without the assumption of a single contracting point. Additionally, it introduces new types of generalized cyclic abc;r contraction mappings and describes the existence of a single fixed point of them in b-metric spaces. Finally, the presented results establish a simpler convergence theorem for a sequence of generalized cyclic abc;r contraction mappings, extend, and generalize some of the previous reported results.
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.
This paper involves complex valued versions of Riemann-Liouville integral, Atangana-Baleanu integral operator and non-linear Telegraph equation. Under various suitable assumptions the results are ...established in the setting of complex valued double controlled metric space. Thereafter, by making consequent use of the fixed point method, short and simple proofs are obtained for solutions of Riemann-Liouville integral, complex valued Atangana-Baleanu integral operator and non-linear Telegraph equation.
The current paper introduces a novel generalization of cone metric spaces called type I and type II composed cone metric spaces. Therefore, examples of a type I and type II composed cone metric ...space, which is not a cone metric space, are given. We establish some results of fixed point precisely about Hardy–Rogers type contraction on C2CMS and provide examples. Finally, we present an application of our results and how our results solve the Fredholm integral equation of generalizing several existing and unique fixed point theorems.
One of the well-studied generalizations of a metric space is known as a partial metric space. The partial metric space was further generalized to the so-called M-metric space. In this paper, we ...introduce the Double-Controlled Quasi M-metric space as a new generalization of the M-metric space. In our new generalization of the M-metric space, the symmetry condition is not necessarily satisfied and the triangle inequality is controlled by two binary functions. We establish some fixed point results, along with the examples and applications to illustrate our results.
In the framework of complete metric spaces, the major objective of this paper is to investigate if a common coincidence point exists for more than two fuzzy mappings meeting the criteria of hybrid ...fuzzy contractions of Nadler’s type in connection with the Hausdorff metric. Fascinating examples are also provided to show how the strategy can be used. For the presence of a common
α
-fuzzy fixed point of three and four fuzzy mappings, we have derived sufficient requirements. Further prior observations are offered as corollaries from the relevant literature. Some implications that are clear in this mode and widely covered in literature are expanded upon and included in our study.
PDF
