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Reseach Article

On the Weak Stability of Picard Iteration for Some Contractive Type Mappings and Coincidence Theorems

by Ioana Timis
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 37 - Number 4
Year of Publication: 2012
Authors: Ioana Timis
10.5120/4595-6549

Ioana Timis . On the Weak Stability of Picard Iteration for Some Contractive Type Mappings and Coincidence Theorems. International Journal of Computer Applications. 37, 4 ( January 2012), 9-13. DOI=10.5120/4595-6549

@article{ 10.5120/4595-6549,
author = { Ioana Timis },
title = { On the Weak Stability of Picard Iteration for Some Contractive Type Mappings and Coincidence Theorems },
journal = { International Journal of Computer Applications },
issue_date = { January 2012 },
volume = { 37 },
number = { 4 },
month = { January },
year = { 2012 },
issn = { 0975-8887 },
pages = { 9-13 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume37/number4/4595-6549/ },
doi = { 10.5120/4595-6549 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:23:25.256509+05:30
%A Ioana Timis
%T On the Weak Stability of Picard Iteration for Some Contractive Type Mappings and Coincidence Theorems
%J International Journal of Computer Applications
%@ 0975-8887
%V 37
%N 4
%P 9-13
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Starting from a weak concept of stability, introduced by Berinde [1] and called “weak stability”, in [27] we develop a weaker notion, named “w²-stability”. Therefore, in this paper we prove some results of this weaker stability concept for certain class of mappings and also we give some examples of w²-stable but not weak stable nor stable iterations. Because of the restriction of an “approximate” sequence, some fixed point iteration procedures are not weakly stable so if it is used a weaker type of sequence, the stability can be obtained in the meaning of a new concept.

References
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Index Terms

Computer Science
Information Sciences

Keywords

Coincidence point fixed point stable iteration weak stable iteration