General implicit variational inclusion problems based on A-maximal (m)-relaxed monotonicity (AMRM) frameworks |
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Authors: | Ravi P. Agarwal Ram U. Verma |
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Affiliation: | a Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA b International Publications (USA), 12085 Lake Cypress Circle, Suite I 109, Orlando, FL 32828, USA |
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Abstract: | A general framework for an algorithmic procedure based on the variational convergence of operator sequences involving A-maximal (m)-relaxed monotone (AMRM) mappings in a Hilbert space setting is developed, and then it is applied to approximating the solution of a general class of nonlinear implicit inclusion problems involving A-maximal (m)-relaxed monotone mappings. Furthermore, some specializations of interest on existence theorems and corresponding approximation solvability theorems on H-maximal monotone mappings are included that may include several other results for general variational inclusion problems on general maximal monotonicity in the literature. |
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Keywords: | Variational inclusions Maximal monotone mapping A-maximal (m)-relaxed monotone mapping Generalized resolvent operator Variational graphical convergence |
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