Bulletin of the Korean Mathematical Society (대한수학회보)

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SYSTEM OF GENERALIZED MULTI-VALUED RESOLVENT EQUATIONS: ALGORITHMIC AND ANALYTICAL APPROACH

  • Javad Balooee (School of Mathematics Statistics and Computer Science College of Science University of Tehran) ;
  • Shih-sen Chang (Center for General Education China Medical University) ;
  • Jinfang Tang (Department of mathematics Yibin University)
  • Received : 2022.05.30
  • Accepted : 2022.11.10
  • Published : 2023.05.31
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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(·, ·)-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(·, ·)-co-accretive mapping is actually P-accretive and is not a new one. In the meanwhile, some important comments on H(·, ·)-co-accretive mappings and the results related to them appeared in the literature are pointed out.

Keywords

Acknowledgement

The authors thank the editor and anonymous reviewers for their valuable comments and suggestions which have improved the final version of the manuscript.

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