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

• Published in: Fixed point theory and algorithms for sciences and engineering Vol. 2012; no. 1; pp. 1 - 13
• Main Author: Ge, Ci-Shui
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 26.04.2012; Springer Nature B.V
• Subjects: Analysis; Applications of Mathematics; Asymptotic properties; Classification; Convergence; Differential Geometry; Inequalities; Iterative algorithms; Mapping; Mathematical analysis; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; Theorems; Topology; monotone mapping; variational inequality; variable coefficient method; asymptotically strict pseudocontractive mapping in the intermediate sense; fixed point
• ISSN: 1687-1812; 1687-1820; 1687-1812; 2730-5422
• DOI: 10.1186/1687-1812-2012-68

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.