An iterated function system consists of a complete metric space (X,d) and finite family contractions f1,⋯,fn:X→X. A generalized comprises defined on the Cartesian product Xm with values in X. In this paper, we want to investigate systems more general setting b-metric spaces. We prove that such admits unique attractor and, under some further restrictions b-metric, it depends continuously paramet...

Abstract In this paper, we improve the Proinov theorem by adding certain rational expressions to definition of corresponding contractions. After that, prove fixed point theorems for these modified contractions in framework dislocated b -metric spaces. We show some illustrative examples indicate validity main results.

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

The aim of this paper is to study induced (quasi-)uniformities in Kramosil and Michalek's fuzzy metric spaces. Firstly, $I$-uniformity in the sense of J. Guti'{e}rrez  Garc'{i}a and $I$-neighborhood system in the sense of H"{o}hle and u{S}ostak are induced by the given fuzzy metric. It is shown that the fuzzy metric and the induced $I$-uniformity will generate the same $I$-neighborhood system. ...