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 {τ, 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 [29] and mf-iterations. we show numerically that the considered iterative scheme converges faster than sokhuma and kaewkhao [29] for single-valued and multi-valued non-expansive mappings. our newly proven results generalize several relevant results in the literature.