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

Müzeyyen Ertürk; Faik Gürsoy

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 1, page 69-83
  • ISSN: 0862-7959

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.

How to cite

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Ertürk, Müzeyyen, and Gürsoy, Faik. "Some convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operators." Mathematica Bohemica 144.1 (2019): 69-83. <http://eudml.org/doc/294646>.

@article{Ertürk2019,
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.},
author = {Ertürk, Müzeyyen, Gürsoy, Faik},
journal = {Mathematica Bohemica},
keywords = {iteration method; quasi-strictly contractive operator; convergence; rate of convergence; stability; data dependency},
language = {eng},
number = {1},
pages = {69-83},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operators},
url = {http://eudml.org/doc/294646},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Ertürk, Müzeyyen
AU - Gürsoy, Faik
TI - Some convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operators
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 1
SP - 69
EP - 83
AB - 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.
LA - eng
KW - iteration method; quasi-strictly contractive operator; convergence; rate of convergence; stability; data dependency
UR - http://eudml.org/doc/294646
ER -

References

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