On interpolative F-contractions with shrink map

Abstract

In this article, we introduce two notions of interpolative F-contractions with shrink map and F-contractions with shrink map. We also study the existence of E-fixed points by using these notations on a metric space endowed with a binary relation. As an application and consequence of the main results, we also get some other interesting results like a common fixed point result, an E-fixed point result on a metric space equipped with graph, and an existence theorem for a solution of integral equations.

Common fixed point theorems for interpolative rational-type mapping in complex-valued metric space

“…Mishra et al [30] proved an interpolative Reich-Rus-Ćirić and Hardy-Rogers contraction on quasi-partial b-metric space and related fixed point results. Alansari and Ali [1] gave the results on interpolative prešić type contractions and related results. Wangwe and Kumar [47] proved fixed point results for interpolative ψ-Hardy-Rogers type contraction mappings in quasi-partial b-metric space with applications.…”

Common fixed point Theorems for Interpolative Mapping in Bicomplex-valued b-Metric Space with An application to Non-linear matrix Equation

“…Mishra et al [19] proved an interpolative Reich-Rus-Ćirić and Hardy-Rogers contraction on quasi-partial b-metric space and related fixed point results. Alansari and Ali [1] gave the results on interpolative prešić type contractions and related results. Wangwe and Kumar [27] proved fixed point results for interpolative ψ -Ψ-Hardy-Rogers type contraction mappings in quasi-partial b-metric space with applications.…”

Common fixed point theorems for interpolative mappings in bicomplex-valued b-metric spaces with an application to non-linear matrix equations

“…Mishra et al [25] introduced an interpolative Reich-Rus-Ciric and Hardy-Rogers contraction on quasipartial b-metric spaces and related fixed point results. Alansari and Ali [1] gave some results on interpolative presic type contractions. Wangwe and Kumar [35] proved fixed point results for interpolative ψ-Hardy-Rogers type contraction mappings in quasi-partial b-metric spaces with applications.…”

“…[23] Let (Υ, d B ) be a complete bicomplex valued b-metric space with coefficient s ≥ 1 and S, T : Υ → Υ. If there exists λ 1 , λ 2 , λ 3 , λ 4 : Υ → [0,1 s ] such that for all ϑ, ∈ Υ;…”