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In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of ¯D. Kurepa, a new approach to fixed point problems, by defining generalized metric spaces (also known as vector valued metric spaces), and providing some actual results for the first time. Using the recent approach of coordinate representation for a generalized metric of Jachymski and Klima, we verify in this article some natural properties of generalized metric spaces, already owned by standard metric spaces. Among other results, we show that the theorems of Nemytckii (1936) and Edelstein (1962) are valid in generalized metric spaces, as well. A new application to fractional differential equations is also presented. At the end we state a few open questions for young researchers. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of interpolative fuzzy Z-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the existing fuzzy contractions (by Gregori et al. [6]), contraction (by Mihet [11]), fuzzy Z-contractions (by Shukla et al. ([19]) and Tirado contraction (by Tirado [20]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in [19] through weak compatibility. As an applications, we discuss fixed point theorem for Fredholm non-linear integral equation. The article also includes an example, which shows the validity of our results. [ABSTRACT FROM AUTHOR]

In this article, we introduce generalized cyclic contractions in the context of metric-like spaces and prove some new fixed point results concerning these contractions. Our results, extend and unify several results in existing literature. We present suitable examples to make our findings worth mentioning. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of F--G--contraction mappings in F-metric spaces endowed with a graph and give some fixed point results for such contractions. Our results are generalization of some famous theorem in metric spaces to F--metric spaces endowed with a graph. Also, we give some examples that support obtained theoretical results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish the uniqueness and existence of the common fixed point under generalized contractive conditions in b -metric spaces with supportive examples. We also approximate the common fixed point by Jungck–Picard and Picard iteration procedures along with the P property of the mappings. Further, (T , f) -stability of Jungck–Picard iterative and T -stability of Picard iterative schemes are proved. [ABSTRACT FROM AUTHOR]

In this paper, we present a new type of contraction calledW-contraction in fuzzy metric space. Utilizing this contraction, we establish a unique fixed point theorem for self-map in the structure of fuzzy metric space which turns out to be generalization of fuzzy contraction given by Gregori et al. [8]. As an application of our result, we study the existence and uniqueness of the solution to nonlinear ordinary differential equations. The article also includes an example which shows the validity of our results. [ABSTRACT FROM AUTHOR]

This paper presents a new and general class of α - K ψ - s-contractions, involving α-admissible and - s simulation mappings considered in the setting of b-metric-like spaces. By applying this set of contractions associated with applications to integral equation, we unify, generalize, and increase the fixed point results range in the literature. [ABSTRACT FROM AUTHOR]