Document Type : Research Paper


Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, 25240, Turkey.


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].


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