N*-Iteration Approach for Approximation of Fixed Points in Uniformly Convex Banach Space

Abstract

In this paper, a new iterative approach for approximating the fixed points (FPs) of Suzuki generalized nonexpansive (SGN) mapping as well as weak contractions, called the N* iteration approach, is presented. Furthermore, it is demonstrated analytically and numerically that the proposed approach converges to an FP for contraction map faster than some well-known and leading approaches. To support the main results, several non-trivial numerical examples are presented. Finally, the stability of the new iterative approach is confirmed. The results of this work improve and extend the corresponding results in the literature.

Keywords

• : converge sequence
• fixed point
• iteration process
• suzuki’s generalized non-expansive mapping
• uniformly convex banach space