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System of generalized variational-like inclusions involving (P,η)-accretive mapping and fixed point problems in real Banach spaces.
- Source :
-
Arabian Journal of Mathematics . Apr2024, Vol. 13 Issue 1, p1-33. 33p. - Publication Year :
- 2024
-
Abstract
- This paper attempts to prove the Lipschitz continuity of the resolvent operator associated with a (P , η) -accretive mapping and compute an estimate of its Lipschitz constant. This is done under some new appropriate conditions that are imposed on the parameter and mappings involved in it; with the goal of approximating a common element of the solution set of a system of generalized variational-like inclusions and the fixed point set of a total asymptotically nonexpansive mapping in the framework of real Banach spaces. A new iterative algorithm based on the resolvent operator technique is proposed. Under suitable conditions, we prove the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the two sets mentioned above. The final section is dedicated to investigating and analyzing the notion of a generalized H(.,.)-accretive mapping introduced and studied by Kazmi et al. (Appl Math Comput 217:9679–9688, 2011). In this section, we provide some comments based on the relevant results presented in their work. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 21935343
- Volume :
- 13
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Arabian Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 175896507
- Full Text :
- https://doi.org/10.1007/s40065-023-00440-1