Algorithmic Aspect and Convergence Analysis for System of Generalized Multivalued Variational-like Inequalities

Javad Balooee, Shih-Sen Chang, Lin Wang and Zhaoli Ma
Additional contact information
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
Zhaoli Ma: College of Public Foundation, Yunnan Open University, Kunming 650223, China

Mathematics, 2022, vol. 10, issue 12, 1-40

Abstract: The main aim of this paper is twofold. Our first objective is to study a new system of generalized multivalued variational-like inequalities in Banach spaces and to establish its equivalence with a system of fixed point problems utilizing the concept of P - η -proximal mapping. The obtained alternative equivalent formulation is used and a new iterative algorithm for finding its approximate solution is suggested. Under some appropriate assumptions imposed on the mappings and parameters involved in the system of generalized multivalued variational-like inequalities, the existence of solution for the system mentioned above is proved and the convergence analysis of the sequences generated by our proposed iterative algorithm is discussed. The second objective of this work is to investigate and analyze the notion M - η -proximal mapping defined in the literature. Taking into account of the assumptions considered for such a mapping, we prove that every M - η -proximal mapping is actually P - η -proximal and is not a new one. At the same time, some comments relating to some existing results are pointed out.

Keywords: system of generalized multivalued variational-like inequalities; graph convergence; P - ? -proximal mapping; iterative algorithm; convergence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/12/2016/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/12/2016/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:12:p:2016-:d:836525

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().