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

Ertürk, Müzeyyen ; Gürsoy, Faik

Mathematica Bohemica, Tome 144 (2019) no. 1, pp. 69-83

Abstract (VO)

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.

Détail

DOI : 10.21136/MB.2018.0085-17

Classification : 47H09, 47H10, 54H25
Keywords: iteration method; quasi-strictly contractive operator; convergence; rate of convergence; stability; data dependency

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