Some convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operators

Abstract

We study some qualitative features like convergence, stability and data dependency for Picard-S iteration method of a quasi-strictly contractive operator under weaker conditions imposed on parametric sequences in the mentioned method. We compare the rate of convergence among the Mann, Ishikawa, Noor, normal-S, and Picard-S iteration methods for the quasi-strictly contractive operators. Results reveal that the Picard-S iteration method converges fastest to the fixed point of quasi-strictly contractive operators. Some numerical examples are given to validate the results obtained herein. Our results substantially improve many other results available in the literature.

Keywords

• iteration method
• quasi-strictly contractive operator
• convergence
• rate of convergence
• stability
• data dependency