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\(H\)-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces. (English) Zbl 1056.49012

Summary: We first introduce a new class of generalized accretive operators named \(H\)-accretive operators in Banach spaces. By studying the properties of \(H\)-accretive operators, we extend the concept of resolvent operators associated with the classical \(m\)-accretive operators to the new \(H\)-accretive operators. In terms of the new resolvent operator technique, we give the approximate solution for a class of variational inclusions involving \(H\)-accretive operators in Banach spaces.

MSC:

49J40 Variational inequalities
47H06 Nonlinear accretive operators, dissipative operators, etc.
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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