Role of Relative A-Maximal Monotonicity in Overrelaxed Proximal-Point Algorithms with Applications
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A general framework for a class of overrelaxed proximal point algorithms based on the notion of relative A-maximal monotonicity is introduced; then, the convergence analysis for solving a general class of nonlinear variational inclusion problems is explored. The framework developed in this communication is quite suitable, unlike other existing notions of generalized maximal monotonicity, including A-maximal (m)-relaxed monotonicity in literature, to generalize first-order nonlinear evolution equations/evolution inclusions based on the generalized nonlinear Yosida approximations in Hilbert spaces as well as in Banach spaces.
KeywordsVariational inclusions Maximal monotone mapping Relative A-maximal monotone mapping Generalized resolvent operator
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