Document Type : Research Paper

Authors

• Asghar Rahimi
• Ali Rezaei
• Bayaz Daraby
• Mostafa Ghasemi

Department of Mathematics, University of Maragheh, Maragheh, Iran

Abstract

In this paper, we introduce a new iterative scheme to approximate the fixed point of generalized α-nonexpansive mappings. we first prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized α-nonexpansive mappings. Using the example presented in [R. Pant and R. Shukla, Approximating fixed point of generalized α-nonexpansive mappings in Banach spaces, J. Numer. Funct. Anal. Optim. 38(2017) 248-266.], we compare the convergence behavior of the new iterative process with other iterative processes.

Keywords

• Uniformly convex Banach space
• Convergence theorem
• Generalized α-nonexpansive mapping
• Opial property
• Iterative process