Fixed Point Results for $F$-Hardy-Rogers Contractions via Mann's Iteration Process in Complete Convex $b$-Metric Spaces

Abstract

In this paper, we give a definition of the $F$-Hardy-Rogers contraction of Nadler type by eliminating the conditions $(F3)$ and $(F4)$. And, we obtain some fixed point theorems for such mappings using Mann's iteration process in complete convex $b$-metric spaces. We also give an example in order to support the main results, which generalize some results in [5,6].

Keywords

• $f$-hardy-rogers contraction
• mann's iteration process
• fixed point
• convex $b$-metric space