Viscosity iterative algorithm for variational inequality problems and fixed point problems in a real q -uniformly smooth Banach space

Fixexd point theory and applications

Gang Cai¹ 

[1] School of Mathematics Science, Chongqing Normal University, Chongqing, China

关键词: strong convergence;    variational inequality;    fixed point;    strict pseudocontraction;    q-uniformly smooth Banach space;    49J30;    47H10;    47H17;    49M05;   

DOI  :  10.1186/s13663-015-0316-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this paper is to study a viscosity iterative algorithm for finding a common element of the set of solutions of a general variational inequality problem for two inverse strongly accretive operators and the set of fixed points of a δ-strict pseudocontraction in a real q-uniformly smooth Banach space. Some strong convergence theorems are obtained under appropriate conditions. As an application, we prove some strong convergence theorems for fixed point problems and variational inequality problems or equilibrium problems in Hilbert spaces. These results improve and extend the corresponding results announced by many others.

【 授权许可】

CC BY