Document Type : Research Paper

Authors

• Fayyaz Rouzkard ¹
• Mohammad Imdad ²

¹ Department of Mathematics, Farhangian University, Tehran, Iran

² Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

Abstract

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 [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.

Keywords

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