Abstract
A new system of nonlinear variational inclusions involving -monotone mappings in the framework of Hilbert space is introduced and then based on the generalized resolvent operator technique associated with -monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since -monotonicity generalizes -monotonicity and -monotonicity, our results improve and extend the recent ones announced by many others.
Highlights
Variational inclusions problems are among the most interesting and intensively studied classes of mathematical problems and have wide applications in the fields of optimization and control, economics and transportation equilibrium, and engineering sciences
Various kinds of iterative algorithms to solve the variational inequalities and variational inclusions have been developed by many authors
Verma 9 generalized the recently introduced and studied notion of A-monotonicity to the case of A, η -monotonicity, while examining the sensitivity analysis for a class of nonlinear variational inclusion problems based on the generalized resolvent operator technique
Summary
Variational inclusions problems are among the most interesting and intensively studied classes of mathematical problems and have wide applications in the fields of optimization and control, economics and transportation equilibrium, and engineering sciences. Verma 9 generalized the recently introduced and studied notion of A-monotonicity to the case of A, η -monotonicity, while examining the sensitivity analysis for a class of nonlinear variational inclusion problems based on the generalized resolvent operator technique. Let M : H→2H be a multivalued mapping from a Hilbert space H to 2H, the power set of H.
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