Geodesic
Some convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operators
Mathematica Bohemica, Tome 144 (2019) no. 1, pp. 69-83

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
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 
@article{10_21136_MB_2018_0085_17,
     author = {Ert\"urk, M\"uzeyyen and G\"ursoy, Faik},
     title = {Some convergence, stability and data dependency results for a {Picard-S} iteration method of quasi-strictly contractive operators},
     journal = {Mathematica Bohemica},
     pages = {69--83},
     publisher = {mathdoc},
     volume = {144},
     number = {1},
     year = {2019},
     doi = {10.21136/MB.2018.0085-17},
     mrnumber = {3934198},
     zbl = {07088836},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0085-17/}
}
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
SP  - 69
EP  - 83
VL  - 144
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0085-17/
DO  - 10.21136/MB.2018.0085-17
LA  - en
ID  - 10_21136_MB_2018_0085_17
ER  - 
%0 Journal Article
%A Ertürk, Müzeyyen
%A Gürsoy, Faik
%T Some convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operators
%J Mathematica Bohemica
%D 2019
%P 69-83
%V 144
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0085-17/
%R 10.21136/MB.2018.0085-17
%G en
%F 10_21136_MB_2018_0085_17
Ertürk, Müzeyyen; Gürsoy, Faik. Some convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operators. Mathematica Bohemica, Tome 144 (2019) no. 1, pp. 69-83. doi: 10.21136/MB.2018.0085-17

Cité par Sources :