Approximation of fixed points for a new class of generalized non-expansive mappings in Banach spaces

In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition $ B_{\gamma, \mu } $. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory.