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A resolvent approach for solving a set-valued variational inclusion problem using weak-RRD set-valued mapping. (English) Zbl 1432.49018

Summary: The resolvent operator approach by I. Ahmad et al. [“The relaxed resolvent operator for solving fuzzy variational inclusion problem involving ordered RME set-valued mapping”, Indian J. Industrial Appl. Math. 10, 255–268 (2019; doi:10.5958/1945-919X.2019.00018.5)] is applied to solve a set-valued variational inclusion problem in ordered Hilbert spaces. The resolvent operator under consideration is called relaxed resolvent operator and we demonstrate some of its properties. To obtain the solution of a set-valued variational inclusion problem, an iterative algorithm is developed and weak-RRD set-valued mapping is used. The problem as well as main result of this paper are more general than many previous problems and results available in the literature.

MSC:

49J53 Set-valued and variational analysis
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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