Common fixed points for hybrid pair of generalized non-expensive mappings by a three-step iterative scheme

In this paper, we introduce a three-step iterative scheme, called the MF-iteration process to approximate a common fixed point for a hybrid pair \{\tau, T\}  of single-valued and multi-valued maps satisfying a generalized contractive condition defined on uniformly convex Banach spaces. We establish the strong convergence theorem for the proposed process under some basic boundary conditions. We give a numerical example to prove our results' convergence rate. Further, we compare the convergence speed of Sokhuma and Kaewkhao [۲۹] and MF-iterations. we show numerically that the considered iterative scheme converges faster than Sokhuma and Kaewkhao [۲۹] for single-valued and multi-valued non-expansive mappings. Our newly proven results generalize several relevant results in the literature.

Keywords:

uniformly convex Banach spaces , Suzuki's Generalized Non-Expansive , Three-step iterative scheme , Common fixed point