System of generalized variational-like inclusions involving $$\varvec{(P,\eta )}$$ ( P , η ) -accretive mapping and fixed point problems in real Banach spaces

Abstract

Abstract This paper attempts to prove the Lipschitz continuity of the resolvent operator associated with a $$(P,\eta )$$ ( 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.

Keywords

• 47H05
• 47H06
• 47H09
• 47J22
• 47J25
• 49J40