A new faster iteration process to fixed points of generalized α-nonexpansive mappings in Banach spaces

Document Type : Research Paper


Department of Mathematics, University of Maragheh, Maragheh, Iran



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.


Articles in Press, Corrected Proof
Available Online from 12 May 2023
  • Receive Date: 01 April 2021
  • Revise Date: 06 August 2021
  • Accept Date: 21 August 2021
  • First Publish Date: 12 May 2023