Nonlinear relaxed cocoercive variational inclusions involving \((A,\eta)\)-accretive mappings in Banach spaces. (English) Zbl 1207.49011

Summary: We introduce a new concept of \((A,\eta)\)-accretive mappings, which generalizes the existing monotone or accretive operators. We study some properties of \((A,\eta)\)-accretive mappings and define resolvent operators associated with \((A,\eta)\)-accretive mappings. By using the new resolvent operator technique, we also construct a new perturbed iterative algorithm with mixed errors for a class of nonlinear relaxed cocoercive variational inclusions involving \((A,\eta)\)-accretive mappings and study applications of \((A,\eta)\)-accretive mappings to the approximation-solvability of this class of nonlinear relaxed cocoercive variational inclusions in \(q\)-uniformly smooth Banach spaces. Our results improve and generalize the corresponding results of recent works.


49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
90C47 Minimax problems in mathematical programming
47H06 Nonlinear accretive operators, dissipative operators, etc.
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