System of Variational Inclusions and Fixed Points of Pseudocontractive Mappings in Banach Spaces

Mathematics

Mihai Postolache¹  Lu-Chuan Ceng²  Xiaolong Qin³  Yonghong Yao⁴ 

[1] Center for General Education, China Medical University, Taichung 40402, Taiwan;Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China;School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China;

关键词: implicit multiple viscosity approximation method;    system of variational inclusions;    pseudocontractive mapping;    nonexpansive mapping;   

DOI  :  10.3390/math7010005

来源: DOAJ

【 摘 要 】

The purpose of this paper is to solve the general system of variational inclusions (GSVI) with hierarchical variational inequality (HVI) constraint, for an infinite family of continuous pseudocontractive mappings in Banach spaces. By utilizing the equivalence between the GSVI and the fixed point problem, we construct an implicit multiple-viscosity approximation method for solving the GSVI. Under very mild conditions, we prove the strong convergence of the proposed method to a solution of the GSVI with the HVI constraint, for infinitely many pseudocontractions.

【 授权许可】

Unknown