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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.

MSC:

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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