Mathematica Bohemica (Apr 2019)

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

  • Müzeyyen Ertürk,
  • Faik Gürsoy

DOI
https://doi.org/10.21136/MB.2018.0085-17
Journal volume & issue
Vol. 144, no. 1
pp. 69 – 83

Abstract

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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