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

• Main Authors: Müzeyyen Ertürk, Faik Gürsoy
• Format: Article
• Language: English
• Published: Institute of Mathematics of the Czech Academy of Science 2019-04-01
• Series: Mathematica Bohemica
• Subjects: iteration method; quasi-strictly contractive operator; convergence; rate of convergence; stability; data dependency
• Online Access: http://mb.math.cas.cz/full/144/1/mb144_1_5.pdf
• ISSN: 0862-7959; 2464-7136

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.