Some results in fixed point theory and application to the convergence of some iterative processes

Fixexd point theory and applications

Abdelkader Dehici¹  Najeh Redjel² 

[1] Department of Mathematics, University of Constantine 1, Constantine, Algeria;Laboratory of Informatics and Mathematics, University of Souk-Ahras, Souk-Ahras, Algeria

关键词: Banach space;    normal structure;    rational expression;    fixed point;    Picard iteration;    Mann iteration;    Ishikawa iteration;    Kirk iteration;    47H09;    47H10;    54H25;   

DOI  :  10.1186/s13663-015-0415-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the existence and uniqueness of fixed points for a class of self-mappings satisfying certain rational expressions on closed, bounded and convex subsets with normal structures in reflexive Banach spaces. We show that, in particular, this class extends that introduced by Ray and Singh (Indian J. Pure Appl. Math. 9:216-221, 1978). As an application, we give an investigation of the convergence and stability of some iterative processes associated to these mappings.

【 授权许可】

CC BY