Graph Convergence, Algorithms, and Approximation of Common Solutions of a System of Generalized Variational Inclusions and Fixed-Point Problems

Javad Balooee, Shih-Sen Chang (), Lin Wang, Yu Zhang and Zhao-Li Ma
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Javad Balooee: School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran 1417935840, Iran
Shih-Sen Chang: Center for General Education, China Medical University, Taichung 40402, Taiwan
Lin Wang: College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
Yu Zhang: College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
Zhao-Li Ma: College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China

Mathematics, 2023, vol. 11, issue 4, 1-29

Abstract: In this paper, under some new appropriate conditions imposed on the parameters and mappings involved in the proximal mapping associated with a general H -monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. The main contribution of this work is the establishment of a new equivalence relationship between the graph convergence of a sequence of general strongly H -monotone mappings and their associated proximal mappings, respectively, to a given general strongly H -monotone mapping and its associated proximal mapping by using the notions of graph convergence and proximal mapping concerning a general strongly H -monotone mapping. By employing the concept of proximal mapping relating to general strongly H -monotone mapping, some iterative algorithms are proposed, and as an application of the obtained equivalence relationship mentioned above, a convergence theorem for approximating a common element of the set of solutions of a system of generalized variational inclusions involving general strongly H -monotone mappings and the set of fixed points of an ( { a n } , { b n } , ϕ ) -total uniformly L -Lipschitzian mapping is proved. It is significant to emphasize that our results are new and improve and generalize many known corresponding results.

Keywords: system of generalized variational inclusions; general H -monotone operator; ({ a n }, { b n }, ? )-total uniformly L -Lipschitzian mapping; proximal mapping; graph convergence; fixed point; convergence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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