Quasi Metric Research Articles

On Ekeland Variational Principle and Its Applications Through Fuzzy Quasi Metric Spaces with Non-Archimedean t-norm

The aim of this article is to introduce Ekeland variational principle (EVP) and some results in fuzzy quasi metric space (FQMS) under the non-Archimedean \(t\)-norms. In this article the basic topological properties and a partial order relation are defined on FQMS. Utilizing Brézis-Browder principle on a partial order set, we extend the EVP to FQMS also. Moreover, we derive Takahashi’s minimization theorem, which ensures the existence of a solution of an optimal problem without taking the help of compactness and convexity properties on the underlying space. Furthermore, we give an equivalence chain between these two theorems. Finally, two fixed point results namely the Banach fixed point and the Caristi-Kirk fixed point theorems are described extensively.

Some Fixed Point Results for α-Admissible mappings on Quasi Metric Space Via θ-Contractions

By employing α-admissible mapping, this study expands and investigates generalized contraction mappings in quasi-metric spaces, aiming to establish the existence of fixed points. Moreover, we show that the main outcomes of the paper encompass several previously reported results in the literature.

A new contribution to best proximity point theory on quasi metric spaces and an application to nonlinear integral equations

In this paper, we first review some important definitions and notions related to best proximity point theory by considering the lack of symmetry property of quasi metric. Then, we introduce a new notion of BG-multivalued contraction mappings. Then, a best proximity point result is obtained via Q-function on quasi metric. Also, we present a noteworthy illustrative example to show the effect of our results. Finally, we give an existence and uniqueness result for the solution of nonlinear integral equations via our result.

A Study on Common Fixed Point of Joint A;B Generalized Cyclic ϕ−abc Weak Nonexpansive Mappings and Generalized Cyclic abc;r Contractions in Quasi Metric Spaces

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.

Fixed Point Theorems on Complete Quasi Metric Spaces Via C-class and A-Class Functions

In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the quasi metric does not provide the symmetry property. Finally, we show that our main results includes many fixed point theorems presented on both complete metric and complete quasi metric spaces in the literature. We also provide an illustrative example to show importance of our results.

Common Fixed Point under Nonlinear Contractions on Quasi Metric Spaces

We introduce in this article the notion of ( ψ , ϕ ) - quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence and uniqueness of the fixed point for a couple functions under that contraction.

Common Fixed Point Results for Rational (α,β)φ-mω Contractions in Complete Quasi Metric Spaces

The ω -distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified ω -distance mapping to introduce the notion of rational ( α , β ) φ - m ω contraction. We utilize our new notion to construct and formulate many fixed point results for a pair of two mappings defined on a nonempty set A. Our results modify many existing known results. In addition, we support our work by an example.

Common Fixed Point Theorems via Implicit Contractions in Soft Quasi Metric Spaces

Some common fixed point results involving implicit contractions on soft quasi metricspaces are presented in this research article. Also, the well posedness property of thecommon fixed point problem of mappings is defined and a theorem is given about it.Finally, some fixed point results on soft G-metric spaces are indicated to be urgentoutcomes of main theorems are given in this article .

English

English

English

English

New Fixed Point Theorem in Dislocated Quasi Metric Space

New Fixed Point Theorem in Dislocated Quasi Metric Space

Common Fixed Point Result in Dislocated Quasi Metric Spaces

Common Fixed Point Result in Dislocated Quasi Metric Spaces

Contribution of Fixed Point Theorem in Quasi Metric Spaces

Contribution of Fixed Point Theorem in Quasi Metric Spaces

Some Generalized Fixed Point Theorems of Contraction Type Mappings in Quasi Metric Spaces

This paper adjusts conditions on new defined given the name {a, d, c; r} ctype of contraction mappings on complete quasi metric space, confirms that there is only one fixed of any of these mappings with these adjustments, extends and generalizes results given in some previous research papers, and then builds a convergence theorem for a sequence of fixed points of {Sn}n∈N;{wn*}n∈N to the unique fixed of S; w, provided that limn→∞ Sn(w) = S(w).

Common Fixed Point Theorem in T0 Quasi Metric Space

In this paper, we prove fixed point theorems for generalized C-contractive and generalized S-contractive mappings in a bi-complete di-metric space. The relationship between q- spherically complete T0 Ultra-quasi-metric space and bi-complete diametric space is pointed out in proposition 5.1. This work is motivated by Petals and Fvidalis in a T0-ultraquasi- metric space 2000 AMS Subject Classification: 47H17, 74H05, 47H09.

Using C-Class Function on Coupled Fixed Point Theorems for Mixed Monotone Mappings in Partially Ordered Rectangular Quasi Metric Spaces

Using C-Class Function on Coupled Fixed Point Theorems for Mixed Monotone Mappings in Partially Ordered Rectangular Quasi Metric Spaces

Some Coupled Fixed Point Theorems in Dislocated Quasi Metric Spaces

In this paper, we study some coupled fixed point theorems in a dislocated quasi-metric space which improve and extend some existing results.

On Dislocated Fuzzy Topologies and Fixed Points

The dislocated topology associated with a Dislocated Fuzzy Quasi Metric Space (DFqM − S pace) is discussed and a generalised common fixed point theorem for two mappings f : X → X and T : X k → X in a DFqM − S pace is proved.