Relatively maximal monotone mappings and applications to general inclusions |
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Authors: | Ravi P Agarwal Ram U Verma |
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Institution: | 1. Department of Mathematical Sciences , Florida Institute of Technology , Melbourne, FL 32910, USA;2. Department of Mathematics and Statistics , King Fahd University of Petroleum and Minerals , Dhahran 31261, Saudi Arabia agarwal@fit.edu;4. Department of Mathematics , Texas A&5. M University – Kingsville , Kingsville, TX 78363, USA |
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Abstract: | Based on the relative maximal monotonicity frameworks, the approximation solvability of a general class of variational inclusion problems is explored, while generalizing most of the investigations on weak convergence using the proximal point algorithm in a real Hilbert space setting. Furthermore, the main result has been applied to the context of the relative maximal relaxed monotonicity frameworks for solving a general class of variational inclusion problems. It seems that the obtained results can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution inclusions, and the obtained results can further be applied to the Douglas–Rachford splitting method for finding the zero of the sum of two relatively monotone mappings as well. |
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Keywords: | inclusion problems maximal monotone mapping relatively maximal monotone mapping generalized resolvent operator |
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