Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2023; 60(3): 785-827

Online first article May 16, 2023      Printed May 31, 2023

https://doi.org/10.4134/BKMS.b220372

Copyright © The Korean Mathematical Society.

System of generalized multi-valued resolvent equations: algorithmic and analytical approach

Javad Balooee, Shih-sen Chang, Jinfang Tang

University of Tehran; China Medical University; Yibin University

Abstract

In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with a $P$-accretive mapping, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the construction of a new iterative algorithm using the resolvent operator technique and Nadler's technique for solving a new system of generalized multi-valued resolvent equations in a Banach space setting. The convergence analysis of the sequences generated by our proposed iterative algorithm under some appropriate conditions is studied. The final section deals with the investigation and analysis of the notion of $H(\cdot,\cdot)$-co-accretive mapping which has been recently introduced and studied in the literature. We verify that under the conditions considered in the literature, every $H(\cdot,\cdot)$-co-accretive mapping is actually $P$-accretive and is not a new one. In the meanwhile, some important comments on $H(\cdot,\cdot)$-co-accretive mappings and the results related to them appeared in the literature are pointed out.

Keywords: System of generalized multi-valued resolvent equations, resolvent operator, system of generalized variational inclusions, iterative algorithm, $H(\cdot,\cdot)$-co-accretive mapping, convergence analysis

MSC numbers: Primary 47H05, 47H09, 47J20, 47J22, 47J25, 49J40

Supported by: This work was financially supported by the Natural Science Foundation of China Medical University, Taichung, Taiwan and the Scientific Research Fund of Yibin University (2021YY03).