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

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].