In this article, we give a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces. This theorem extends, unifies and generalizes several well known comparable results in the existing literature.

In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce $(\phi ,F)$ -weak contraction and establish the corresponding fixed point result. Using our new approach for the proof that a Picard sequence is a Cauchy in metric space, our obtained results complement and enrich several methods in the existing literature. At the end we give one open question for F-contraction of Ćirić-type mapping.

In the paper, we consider some fixed point results of $\mathcal{F}$-contractions for triangular $\alpha$-admissible and triangular weak $\alpha$-admissible mappings in metric-like spaces. The results on $\mathcal{F}$-contraction type mappings in the context of metric-like spaces are generalized, improved, unified, and enriched. We prove the main result but using only the property ($\mathcal{F}1$) of the strictly increasing mapping $\mathcal{F}:\left(0,,,+,\infty \right)\to \left(-,\infty ,,,+,\infty \right)$. Our approach gives a proper generalization of several results given in current literature.

Jaradat has proven some fixed point results using JS-G-contraction on $G-$metric spaces. Choudhury et al. were derived coupled fixed point theorems for the $G-$metric spaces. The purpose of this paper is to prove some coupled fixed point theorems of JS-G-contraction on G-metric spaces. Moreover, some example is presented to illustrate the validity of our results.

This paper is dedicated to the memory of the esteemed Serbian mathematician Slaviša B. Prešić (1933–2008). The primary aim of this survey paper is to compile articles on Prešić-type mappings published since 1965. Additionally, it introduces a novel class of symmetric contractions known as Prešić–Menger and Prešić–Ćirić–Menger contractions, thereby enriching the literature on Prešić-type mappings. The paper endeavors to furnish young researchers with a comprehensive resource in functional and nonlinear analysis. The relevance of Prešić’s method, which generalizes Banach’s theorem from 1922, remains significant in metric fixed point theory, as evidenced by recent publications. The overview article addresses the growing importance of Prešić’s approach, coupled with new ideas, reflecting the ongoing advancements in the field. Additionally, the paper establishes the existence and uniqueness of fixed points in Menger spaces, contributing to the filling of gaps in the existing literature on Prešić’s works while providing valuable insights into this specialized domain.

In this article, we generalize, improve, unify and enrich some results for Jaggi-$\mathcal{W}$-contraction-type mappings in the framework of b-metric-like spaces. Our results supplement numerous methods in the existing literature, and we created new approach to prove that a Picard sequence is Cauchy in a b-metric-like space. Among other things, we prove Wardowski’s theorem, but now by using only the property ($\mathcal{W}$1). Our proofs in this article are much shorter than ones in recently published papers.