Abstract
Abstract In this paper, we develop a new perturbed iterative algorithm framework with errors based on the variational graphical convergence of operator sequences with (A, η)-accretive mappings in Banach space. By using the generalized resolvent operator technique associated with (A, η)-accretive mappings, we also prove the existence of solutions for a class of generalized nonlinear relaxed cocoercive operator equation systems and the variational convergence of the sequence generated by the perturbed iterative algorithm in q-uniformly smooth Banach spaces. The obtained results improve and generalize some well-known results in recent literatures. 2000 Mathematics Subject Classification: 47H05; 49J40
Highlights
1 Introduction It is well known that standard Yosida regularizations/approximations have been tremendously effective to approximation solvability of general variational inclusion problems in the context of resolvent operators that turned out to be nonexpansive
It is well known that variational inequalities and variational inclusions provide mathematical models to some problems arising in economics, mechanics, and engineering science and have been studied extensively
We construct a new perturbed iterative algorithm framework with errors based on the variational graphical convergence of operator sequences with (A, h)-accretive mappings in Banach space for approximating the solutions of the nonlinear equation system (1.1) in smooth Banach spaces and prove the existence of solutions and the variational convergence of the sequence generated by the perturbed iterative algorithm in q-uniformly smooth Banach spaces
Summary
It is well known that standard Yosida regularizations/approximations have been tremendously effective to approximation solvability of general variational inclusion problems in the context of resolvent operators that turned out to be nonexpansive.
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