Fixed points of some F-contractions using Mann's iteration in $(\theta,\delta)$-convex $b$-metric spaces

Abstract

This paper presents some fixed-point results in $b$-metric spaces using Mann's iterative process with $(\theta,\delta)$-convex structure. We establish some fixed-point theorems by defining new contraction conditions, namely the F-Kannan type contraction in $(\theta,\delta)$-convex $b$-metric spaces and the F-Hardy Rogers type contraction in $(\theta,\delta)$-convex $b$-metric spaces.