The modification of system of variational inequalities for fixed point theory in Banach spaces

Fixexd point theory and applications

Atid Kangtunyakarn¹ 

[1] Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

关键词: nonexpansive mapping;    strictly pseudo-contractive mapping;    the modification of system of variational inequalities problems;   

DOI  :  10.1186/1687-1812-2014-123

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we use methods different from extragradient methods to prove a strong convergence theorem for the sets of fixed points of two finite families of nonexpansive and strictly pseudo-contractive mappings and the set of solutions of modification of a system of variational inequalities problems in a uniformly convex and 2-uniformly smooth Banach space. Applying the main result we obtain a strong convergence theorem involving two sets of solutions of variational inequalities problems introduced by Aoyama et al. (Fixed Point Theory Appl. 2006:35390, 2006, doi:10.1155/FPTA/2006/35390) in a uniformly convex and 2-uniformly smooth Banach space. We also give a numerical example to support our result.

【 授权许可】

CC BY