Approximation of solutions to a general system of variational inclusions in Banach spaces and applications

Volume 11, Issue 5, pp 644--657 http://dx.doi.org/10.22436/jnsa.011.05.06

Publication Date: March 31, 2018 Submission Date: July 10, 2017 Revision Date: January 02, 2018 Accteptance Date: January 05, 2018

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Authors

Hongbo Liu - School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China. Qiang Long - School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China. Yi Li - School of Science, Southwest University of Science and Technology, China.

Abstract

In this paper, a general system of variational inclusions in Banach Spaces is introduced. An iterative method for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings and common set of fixed points for a \(\lambda\)-strict pseudocontraction is established. Under certain conditions, by forward-backward splitting method, we prove strong convergence theorems in uniformly convex and 2-uniformly smooth Banach spaces. The results presented in the paper improve and extend various results in the existing literatures. Moreover, some applications to monotone variational inequality problem and convex minimization problem are presented.

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Keywords

• General system of variational inclusions
• forward-backward splitting method
• invex set
• resolvent operator
• strictly pseudocontractive

MSC

•  47J05
•  47H09
•  49J25

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