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

Lu-Chuan Ceng, Mihai Postolache, Xiaolong Qin and Yonghong Yao
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Lu-Chuan Ceng: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Mihai Postolache: Center for General Education, China Medical University, Taichung 40402, Taiwan
Xiaolong Qin: Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Yonghong Yao: School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China

Mathematics, 2018, vol. 7, issue 1, 1-14

Abstract: 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.

Keywords: implicit multiple viscosity approximation method; system of variational inclusions; pseudocontractive mapping; nonexpansive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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