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A system of nonlinear variational inclusions with (A, η)-monotone mappings in Hilbert spaces

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In this paper, we introduce a system of nonlinear variational inclusions involving (A, η)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, η)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Our results improve and extend the recent ones announced by many others.

Abstract

In this paper, we introduce a system of nonlinear variational inclusions involving (A, η)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, η)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Our results improve and extend the recent ones announced by many others.

참고문헌 (9)

  1. R. P. Agarwal, "Sensitivity analysis for strongly nonlinear quasi-variational inclusions", Appl. Math. Lett, 13, pp.19~24 (2000)
  2. Y. P. Fang, "H-monotone operator and resolvent operator technique for variational incluisons", Appl. Maht. Comput, 145, pp.795~803 (2003)
  3. Y. P. Fang, "H-monotone operators and system of variational inclus", Commun. Appl. Nonlinear Anal, 11, pp.93~101 (2004)
  4. N. J. Huang, "new clas of general variational inclusions involving maximal ´-monotone mappings", Publ. Math. Debrecen, 62, pp.83~98 (2003)
  5. R. U. Verma, "Sensitivity analysis for generalized strongly monotone variatonal inclu-sions based on the (A; ´)-resolvent operator technique", Appl. Math. Lett, 19, pp.1409~1413 (2006)
  6. R. U. Verma, "Sensitivity analysis for relaxed cocoercive nonlinear quasivariational in- clusions", J. Appl. Math. Stoch. Anal, pp.9~ (2006)[DOI]
  7. R. U. Verma, "A-monotonicity and applications to nonlinear variational inclusion prob-lems", J. Appl. Math. Stoch. Anal, 17, pp.193~195 (2004)
  8. Ram U. Verma, "Approximation-solvability of a class of a-monotone variational inclusion problems", Journal of the Korean Society for Industrial and Applied Mathematics, 8(1), pp.55~66 (2004), 한국산업응용수학회
  9. R. U. Verma, "Approximation solvability of a class of nonlinear set-valued variational inclusions involving (A; ´)-monotone mappings", J. Math. Anal. Appl, 337, pp.969~975 (2008)

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