The purpose of this paper is to introduce a new type of contraction called fuzzy F-contraction. As compared to the F-contraction in the existing literature, our fuzzy F-contraction is much simpler and more straightforward, since it contains only one condition—that is, the function F is strictly increasing. Moreover, some fixed-point theorems for fuzzy F-contraction are presented. Further, some examples are given to illustrate its validity and superiority. In addition, by applying a very significant lemma, we show that our proofs of most fixed-point theorems are shorter and more elegant than ones in the literature.

The main aim of the current paper is the investigation of possibilities for improvements and generalizations contractive condition of Ćirić in the fuzzy metric spaces. Various versions of fuzzy contractive conditions are studied in two directions. First, motivated by recent results, more general contractive conditions in fuzzy metric spaces are achieved and secondly, quasi-contractive type of mappings are investigated in order to obtain fixed point results with a wider class of t-norms.

In this paper, we prove some common fixed point results for four mappings satisfying generalized contractive condition in S-metric space. Our results extend and improve several previous works.

The purpose of this paper is to consider various results in the context of G ${}_b$ -metric spaces that have been recently published after the paper (Aghajani, A.; Abbas, M.; Roshan, J.R. Common fixed point of generalized weak contractive mappings in partially ordered G ${}_b$ -metric spaces. Filomat 2014, 28, 1087–1101). Our new results improve, complement, unify, enrich and generalize already well known results on G ${}_b$ -metric spaces. Moreover, some coupled and tripled coincidence point results have been provided.

In this paper we prove the existence of the unique fixed point for the pair of weakly compatible self-mappings satisfying some Ф-type contractive conditions in the framework of S-metric spaces. Our results generalize, extend, unify, complement and enrich recently fixed point results in existing literature.