M-metric Spaces Research Articles

Fixed Point Theorems in Symmetric Controlled M-Metric Type Spaces

One of the frequently studied approaches in metric fixed-point theory is the generalization of the used metric space. Under this approach, in this study, we introduce a new extension of M-metric spaces, called controlled M-metric spaces, achieved by modifying the triangle inequality and keeping the symmetric condition of the space. The investigation focuses on exploring fundamental properties of this newly defined space, incorporating topological aspects. Several fixed-point theorems and fixed-circle results are established within these spaces complemented by illustrative examples to demonstrate the implications of our findings. Moreover, we present an application involving high-degree polynomial equations.

On the existence of m-norms in vector spaces over valued fields

Gähler (Untersuchungen über verallgemeinerte m-metrische Räume. I”. German. Math Nachr 40, 165–189, 1969) investigated m-metric spaces and in particular m-normed spaces over the field of reals. Here the existence of m-norms will be investigated and this in the more general setting of vector spaces over arbitrary non-trivial valued fields.

On Relational Weak Fℜm,η-Contractive Mappings and Their Applications

In this article, we introduce the concept of weak Fℜm,η-contractions on relation-theoretic m-metric spaces and establish related fixed point theorems, where η is a control function and ℜ is a relation. Then, we detail some fixed point results for cyclic-type weak Fℜm,η-contraction mappings. Finally, we demonstrate some illustrative examples and discuss upper and lower solutions of Volterra-type integral equations of the form ξα=∫0αAα,σ,ξσmσ+Ψα,α∈0,1.

Meir–Keeler Type Contraction in Orthogonal M-Metric Spaces

In this article, we prove fixed point results for a Meir–Keeler type contraction due to orthogonal M-metric spaces. The results of the paper improve and extend some recent developments in fixed point theory. The extension is assured by the concluding remarks and followed by the main theorem. Finally, an application of the main theorem is established in proving theorems for some integral equations and integral-type contractive conditions.

Fixed-Point Results for Meir–Keeler Type Contractions in Partial Metric Spaces: A Survey

In this paper, we aim to review Meir–Keeler contraction mappings results on various abstract spaces, in particular, on partial metric spaces, dislocated (metric-like) spaces, and M-metric spaces. We collect all significant results in this direction by involving interesting examples. One of the main reasons for this work is to help young researchers by giving a framework for Meir Keeler’s contraction.

Compactness and completeness properties of M-metric spaces

An M-metric space is a generalization of a partial metric space. There have been some research investigating the relations between partial metric spaces and M-metric spaces. Theorems and properties prevailing in partial metric spaces are extended in M-metric spaces. In this paper, we study some compactness and completeness properties in M-metric spaces based on the similar properties in partial metric spaces. We also give completeness relation between M-metric spaces and partial metric spaces.

Orthogonal m-metric spaces and an application to solve integral equations

In this article, we introduce the concept of orthogonal m-metric space and prove some fixed point theorems in this space. Furthermore, we obtain results that extend and improve certain comparable results in the existing literature. Eventually, our results lead us to the existence and uniqueness of solutions for Fredholm integral equations.

Recent Fixed-Point Results forθ−Contraction Mappings in RectangularM−Metric Spaces with Supportive Application

The goal of this manuscript is to present a new fixed-point theorem onθ−contraction mappings in the setting of rectangular M-metric spaces (RMMSs). Also, a nontrivial example to illustrate our main result has been given. Moreover, some related sequences withθ−contraction mappings have been discussed. Ultimately, our theoretical result has been implicated to study the existence and uniqueness of the solution to a nonlinear integral equation (NIE).

A Discussion on the Existence of Best Proximity Points That Belong to the Zero Set

In this paper, we investigate the existence of best proximity points that belong to the zero set for the α p -admissible weak ( F , φ ) -proximal contraction in the setting of M-metric spaces. For this purpose, we establish φ -best proximity point results for such mappings in the setting of a complete M-metric space. Some examples are also presented to support the concepts and results proved herein. Our results extend, improve and generalize several comparable results on the topic in the related literature.

Non-Archimedean Fuzzy M-Metric Space and Fixed Point Theorems Endowed with a Reflexive Digraph

Motivated by the concepts of fuzzy metric and m-metric spaces, we introduced the notion of Non- Archimedean fuzzy m-metric space which is an extension of partial fuzzy metric space. We present some examples in support of this new notion. Regarding this notion, its topological structure and some properties are specified simultaneously. At the end, some fixed point results are also provided.

Caristi-Type Fixed Point Theorems and Some Generalizations on M-Metric Space

In this paper, taking into account Caristi’s fixed point results on both metric spaces and partial metric spaces, we present their some extensions and generalizations on M-metric spaces. First, by providing a counter example, we noticed that a recent result on Caristi-type fixed point theorem on M-metric space is not suitable. Then we propounded two versions of Caristi’s inequality and proved some related fixed point results on M -metric space.

Nadler and Kannan Type Set Valued Mappings in M-Metric Spaces and an Application

This article intends to initiate the study of Pompeiu–Hausdorff distance induced by an M-metric. The Nadler and Kannan type fixed point theorems for set-valued mappings are also established in the said spaces. Moreover, the discussion is supported with the aid of competent examples and a result on homotopy. This approach improves the current state of art in fixed point theory.

Two fixed point results for multivalued F-contractions on M-metric spaces

In this article, by considering Feng–Liu’s technique, we present new fixed point results for multivalued mappings which are regarding to F-contraction on M-complete M-metric space. Then, we provide some nontrivial examples showing that our main results proper extension of some earlier results in the literature.

F(psi,varphi)-Contractions for \u03b1-admissible mappings on M-metric spaces

In this paper, we introduce certain α-admissible mappings which are F(psi,varphi)-contractions on M-metric spaces, and we establish some fixed point results. Our results generalize and extend some well-known results on this topic in the literature.

A new generalization of metric spaces: rectangular M-metric spaces

In this paper, we introduce the concept of the rectangular M-metric spaces, along with its topology and we prove some fixed-point theorems under different contraction principles with various techniques. The obtained results generalize some classical fixed-point results such as the Banach’s contraction principle, the Kannan’s fixed-point theorem and the Chatterjea’s fixed-point theorem. Also we give an application to the fixed-circle problem.

Fixed Points for Meir-Keeler Type Contractions in M-Metric Spaces with Applications

Fixed Points for Meir-Keeler Type Contractions in M-Metric Spaces with Applications

F m -contractive and F m-expanding mappings in M-metric spaces

F m -contractive and F m-expanding mappings in M-metric spaces

Partial answers of the Asadi et al.’s open question on [formula omitted]-metric spaces with numerical results

In 2014, Asadi et al. introduced the concept of an M-metric space which is a generalization of a partial metric space and established Banach and Kannan fixed point theorems on M-metric spaces. In this work, we prove two fixed point theorems for Chatterjea contraction mappings in the framework of M-metric spaces. These provide partial answers to a question posed by Asadi et al. concerning a fixed point for Chatterjea contraction mappings. We also give some examples and numerical results which can be obtained from our results.

Fixed point results for multivalued mappings of Feng-Liu type on M-metric spaces

Fixed point results for multivalued mappings of Feng-Liu type on M-metric spaces

Fixed point theorems for Meir-Keeler type mappings in M-metric spaces with applications

AbstractIn this paper, we establish some fixed point theorems for a Meir-Keeler type contraction in M-metric spaces via Gupta-Saxena type contraction. Also, we extend and improve very recent results in fixed point theory.