Strong convergence of iterative algorithms with variable coefficients for asymptotically strict pseudocontractive mappings in the intermediate sense and monotone mappings

Fixexd point theory and applications

Ci-Shui Ge¹ 

[1] Department of Mathematics and Physics, Anhui University of Architecture, Anhui, People's Republic of China

关键词: fixed point;    variational inequality;    asymptotically strict pseudocontractive mapping in the intermediate sense;    monotone mapping;    variable coefficient method;   

DOI  :  10.1186/1687-1812-2012-68

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we propose some iterative algorithms with variable coefficients for finding a common element of the set of fixed points of a uniformly continuous asymptotically κ-strict pseudocon-tractive mapping in the intermediate sense and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. Some strong convergence theorems of these iterative algorithms are obtained without some boundedness assumptions and without some convergence condition. The results of the article improve and extend the recent results of Ceng and Yao, Nadezhkina and Takahashi, and several others. Mathematics Subject Classification (2000): 47H09; 47J20.

【 授权许可】

CC BY