COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS BY A NEW ONE-STEP ITERATION PROCESS

Document Type: Regular Paper

Authors

1 Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar

2 Department of Mathematics, Lahore University of Management Sciences, 54792, Lahore, Pakistan

3 King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran 31261, Saudi Arabia

Abstract

We introduce a new one-step iteration process to approximate common fixed points of two
nonexpansive mappings in Banach spaces and prove weak convergence of the iterative sequence using (i)
Opial’s condition and (ii) Kadec-Klee property. Strong convergence theorems are also established in Banach
spaces and uniformly convex Banach spaces under the so-called Condition ( A ), which is weaker than
compactness.

Keywords