Strong convergence results for variational inclusions, systems of variational inequalities and fixed point problems using composite viscosity implicit methods. (9th December 2022)

• Record Type: Journal Article
• Authors: Wang, Dan-Qiong; Zhao, Tu-Yan; Ceng, Lu-Chuan; Yin, Jie; He, Liang; Fu, Yi-Xuan
• Is Part Of: Optimization. Volume 71:Number 14(2022)
• Page Start: 4177
• Page End: 4212
• Publication Date: 2022-12-09
• Subjects: Composite viscosity implicit method -- system of variational inequalities -- variational inclusions -- W-mappings -- strong convergence; 49J30 -- 47H09 -- 47J20 -- 49M05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1939338
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Let the VI indicate a variational inclusion, the CFPP denote a common fixed point problem of countably many nonexpansive mappings, and the SVI represent a system of variational inequalities. We introduce a composite viscosity implicit method for solving the VI and CFPP with the SVI constraint in the framework of uniformly convex and q -uniformly smooth Banach space where 1 < q ≤ 2 . Moreover, we prove the strong convergence of the sequences generated by the proposed implicit method to a solution of a certain hierarchical variational inequality (HVI). In addition, our results are also applied for solving the fixed point problem (FPP) of nonexpansive mapping, variational inequality problem, convex minimization problem and split feasibility problem in Hilbert spaces.