Strong convergence theorems of nonlinear operator equations for countable family of multi-valued total quasi-phi-asymptotically nonexpansive mappings with applications

作者：Chang Shih Sen^*; Wang Lin; Tang Yong Kun; Zhao Yun He; Ma Zao Li

来源：Fixed Point Theory and Applications, 2012, 69.

DOI：10.1186/1687-1812-2012-69

• multi-valued total quasi-phi-asymptotically nonexpansive mappings
• quasi-phi-asymptotically nonexpansive multi-valued mappings
• quasi-phi-nonexpansive multi-valued mappings
• relatively nonexpansive multi-valued mappings
• generalized projection

The purpose of this article is first to introduce the concept of total quasi-I center dot-asymptotically nonexpansive multi-valued mapping which contains many kinds of mappings as its special cases, and then by using the hybrid shrinking technique to propose an iterative algorithm for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a countable family of multi-valued total quasi-I center dot-asymptotically nonexpansive mappings in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the article not only generalize some recent results from single-valued mappings to multi-valued mappings, but also improve and extend the main results of Homaeipour and Razani.
2000 AMS Subject Classification: 47J06; 47J25.

• 出版日期2012
• 单位云南师范大学; 云南大学