A New and Faster Iterative Scheme Including Generalized $alpha$-nonexpansive Mappings in Banach Spaces

Author(s):

Asghar Rahimi , Ali Rezaei , Bayaz Daraby , Mostafa Ghasemi *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
In this paper, we proposed a new iterative process to approximate fixed point of generalized $alpha$-nonexpansivemappings and show that the coefficient used in the proposed iterative process play a fundamental role in the rate of convergence. We compare the speed of convergence of new iterative process  with other well-known iterative process by using numerical examples. Finally, by using new iterative process, we obtained some weak and strong convergence theorems for generalized $alpha$-nonexpansive mappings in a  Banach space.
Keywords:

Uniformly convex Banach space , Weak convergence , strong convergence , Generalized $alpha$-nonexpansive mapping , Iterative process , Quasi-nonexpansive mapping

Language:
English
Published:
Sahand Communications in Mathematical Analysis, Volume:19 Issue: 2, Spring 2022
Pages:
91 to 111
https://www.magiran.com/p2458618