Research Article
On the Weak Stability of Picard Iteration for Some Contractive Type Mappings and Coincidence Theorems
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 37 - Issue 4 |
| Published: January 2012 |
| Authors: Ioana Timis |
10.5120/4595-6549
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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 },
year = { 2012 },
volume = { 37 },
number = { 4 },
pages = { 9-13 },
doi = { 10.5120/4595-6549 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2012
%A Ioana Timis
%T On the Weak Stability of Picard Iteration for Some Contractive Type Mappings and Coincidence Theorems%T
%J International Journal of Computer Applications
%V 37
%N 4
%P 9-13
%R 10.5120/4595-6549
%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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