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Jleli and Samet in [On a new generalization of metric spaces, J. Fixed Point Theory Appl. 20 (2018), 128 (20 pages)] introduced the notion of ℱ -metric space as a generalization of traditional metric space and proved Banach contraction principle in the setting of this generalized metric space. The objective of this article is to use ℱ -metric space and establish some common fixed point theorems for (β\beta -ψ\psi )-contractions. Our results expand, generalize, and consolidate several known results in the literature. As applications of the main result, the solution for fuzzy initial-value problems in the background of a generalized Hukuhara derivative was discussed.

The aim of this article is to introduce α\alpha -ψ\psi -proximal contraction in the setting of ℱ-metric space and prove the existence of best proximity points for these contractions. As applications of our main results, we obtain coupled best proximity points on ℱ-metric space equipped with an arbitrary binary relation.

This manuscript's main goal is to examine the presence of fixed points in the context of controlled metric‐type spaces utilizing rational type Ćirić‐contractive conditions. We provide appropriate examples to support the validity and superiority of our conclusions. In the context of extended b‐metric space, b‐metric spaces, and standard metric spaces, our findings extrapolate and expand a number of well‐known research findings. As an application of our findings, we prove that a second‐order differential equation has a solution. The paper ends with a few open problems for further investigation of additional dimensions within this framework. [ABSTRACT FROM AUTHOR]

Metric fixed-point theory has become an essential tool in computer science, communication engineering and complex systems to validate the processes and algorithms by using functional equations and iterative procedures. The aim of this article is to obtain common fixed point results in a bicomplex valued metric space for rational contractions involving control functions of two variables. Our theorems generalize some famous results from literature. We supply an example to show the originality of our main result. As an application, we develop common fixed point results for rational contractions involving control functions of one variable in the context of bicomplex valued metric space. [ABSTRACT FROM AUTHOR]

This paper aims to define rational type (αΘ)-contraction in controlled metric space and obtain some advanced fixed point theorems. The outcomes generalize and extend various famous results in the literature. An example and certain consequences are presented to illustrate the significance of established results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define ... and establish some new fixed point theorems in the setting of left K-complete T1-quasi metric space. Our theorems generalize, extend, and unify several results of literature. [ABSTRACT FROM AUTHOR]

The aim of this article is to define Kannan type contraction in the setting of controlled metric space and establish some contemporary fixed point theorems. These results extend several familiar results of literature. An example and certain consequences are presented to illustrate significance of established results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove common fixed point theorems for compatible mappings of type (A) for three self-mappings satisfying certain contractive conditions and its topological properties in partial metric spaces. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce new family of functions M(S; T) and N(S; T) and obtain some new common fixed point theorems in the context of multiplicative metric spaces. The established results carry some well known results from the literature to multiplicative metric space. [ABSTRACT FROM AUTHOR]