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- Title
System of generalized variational-like inclusions involving (P,η)-accretive mapping and fixed point problems in real Banach spaces.
- Authors
Balooee, Javad; Al-Homidan, Suliman
- 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.
- Subjects
NONEXPANSIVE mappings; BANACH spaces; RESOLVENTS (Mathematics); LIPSCHITZ continuity; POINT set theory
- Publication
Arabian Journal of Mathematics, 2024, Vol 13, Issue 1, p1
- ISSN
2193-5343
- Publication type
Article
- DOI
10.1007/s40065-023-00440-1