본문 바로가기
KERD
논문KCI 등재

On nonlinear variational inclusions with (A,η)-monotone mappings

Yan Hao
영남수학회 (Youngnam Mathematical Society)|2009.06|East Asian Mathematical Journal|제25권 제2호|pp. 159-169

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

maximal monotone mapping(Aresolvent operator techniqueη)-monotone mappingvariational inclusions
주제분류수학

초록

In this paper, we introduce a generalized system of nonlinear relaxed co-coercive 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, we consider the approximation solvability of solutions to the generalized system. Since (A,η)-monotonicity generalizes A-monotonicity and H-monotonicity, The results presented this paper improve and extend the corresponding results announced by many others.

Abstract

In this paper, we introduce a generalized system of nonlinear relaxed co-coercive 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, we consider the approximation solvability of solutions to the generalized system. Since (A,η)-monotonicity generalizes A-monotonicity and H-monotonicity, The results presented this paper improve and extend the corresponding results announced by many others.

참고문헌 (26)

  1. R. P. Agarwal, "Sensitivity analysis for strongly nonlinear quasi-variational inclusions", Appl. Math. Lett, 13, pp.19~24 (2000)
  2. Y. J. Cho, "Generalized nonlinear random (A;η)-accretive equations with random relaxed cocoercive mappings in Banach spaces", Comput. Math. Appl, 55, pp.2173~2182 (2008)
  3. Y. J. Cho, "Solvability of implicit complementarity problems", Math. Comput. Model, 45, pp.1001~1009 (2007)
  4. Y. J. Cho, "Generalized nonlinear random (A;η)-accretive equations with random relaxed cocoercive mappings in Banach spaces", Comput. Math. Appl, 55, pp.2173~2182 (2008)
  5. X. P. Ding, "Parametric completely generalized mixed implicit quasi-variational inclu- sions involving H-maximal monotone mappings", J. Comput. Appl. Math, 182, pp.252~269 (2005)
  6. Y. P. Fang, "H-monotone operator and resolvent operator technique for variational incluisons", Appl. Maht. Comput, 256, pp.795~803 (2003)
  7. Y. P. Fang, "H-monotone operators and system of variational inclusions", Commun. Appl. Nonlinear Anal, 11, pp.93~101 (2004)
  8. Y. P. Fang, "A new system of variational inclusions with (H;η)-monotone operators in Hilbert spaces", Comput. Math. Appl, 49, pp.365~374 (2005)
  9. Y. P. Fang, "H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces", Appl. Math. Lett, 17, pp.647~653 (2004)
  10. N. J. Huang, "A new clas of general variational inclusions involvig maximal η-monotone mappings", Publ. Math. Debrecen, 62, pp.83~98 (2003)
  11. N. J. Huang, "A new class of generalized set-valued implicit variational inclusions in banach spaces with an application", Comput. Math. Appl, 41, pp.937~943 (2001)
  12. H. Y. Lan, "On a new system of nonlinear A-monotone multi- valued variational inclusions", J. Math. Anal. Appl, 327, pp.481~493 (2007)
  13. M. A. Noor, "Some resolvent iterative methods for variational inclusions and nonexpansive mappings", Appl. Math. Appl, 194, pp.267~275 (2007)
  14. M. A. Noor, "An iterative scheme for a class of quasi variational inequalities", J. Math. Anal. Appl, 110, pp.463~468 (1985)
  15. X. Qin, "General Wiener-Hopf equation technique for nonexpansive mappings and general variational inequalities in Hilbert spaces", Appl. Math. Comput, 201, pp.716~722 (2008)
  16. X. Qin, "Generalized variational inequalities involving relaxed monotone mappings and nonexpansive mappings", J. Inequal. Appl, 2007 (2007)
  17. X. Qin, "variational inequalities involving relaxed monotone mappings in Hilbert spaces", PamAmer. Math. J, 17, pp.81~88 (2007)
  18. X. Qin, "Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces", Appl. Anal, 87, pp.421~430 (2008)
  19. X. Qin, "Strong convergence of a general iterative method for variational inequality problems and xed point problems in Hilbert spaces", Appl. Math. Comput, 200, pp.242~253 (2008)
  20. R. U. Verma, "Sensitivity analysis for generalized strongly monotone variatonal inclu- sions based on the (A;η)-resolvent operator technique", Appl. Math. Lett, 19, pp.1409~1413 (2006)
  21. R. U. Verma, "Sensitivity analysis for relaxed cocoercive nonlinear quasivariational in- clusions", J. Appl. Math. Stoch. Anal, 2006 (2006)
  22. R. U. Verma, "A-monotonicity and applications to nonlinear variational inclusion prob-lems", J. Appl. Math. Stoch. Anal, 17, pp.193~195 (2004)
  23. R. U. Verma, "Approximation solvability of a class of A-monotone variational inclusion problems", J. KSIAM, 8, pp.55~66 (2004)
  24. R. U. Verma, "A-monotonicity and its role in nonlinear variational inclusions", J. Optim. Theory Appl, 129, pp.457~467 (2006)
  25. R. U. Verma, "A-monotone nonlinear relaxed cocoercive variational inclusions", Central European J. Math, 5, pp.386~396 (2007)
  26. R. U. Verma, "Approximation solvability of a class of nonlinear set-valued variational inclusions involving (A;η)-monotone mappings", J. Math. Anal. Appl, 337, pp.969~975 (2007)

관련 논문AI추천

A system of nonlinear variational inclusions with (A, η)-monotone mappings in Hilbert spacesMeijuan Shang, Xiaolong Qin영남수학회 · East Asian Mathematical Journal2008 · 제24권 제1호GENERAL NONLINEAR VARIATIONAL INCLUSIONS WITH H-MONOTONE OPERATOR IN HILBERT SPACES강신민, Pingping Zheng, Tao Cai, Zeqing Liu대한수학회 · 대한수학회보2010 · 제47권 제2호A SYSTEM OF NONLINEAR VARIATIONAL INCLUSIONS WITH GENERAL H-MONOTONE OPERATORS IN BANACH SPACES강신민, 조민형, Jinsong Li, Wei Wang영남수학회 · East Asian Mathematical Journal2010 · 제26권 제5호ON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h, η)-PROXIMAL MAPPING강신민, 심수학, Zeqing Liu, Zhengsheng Chen대한수학회 · 대한수학회지2008 · 제45권 제5호General framework for proximal point algorithms on (A, η)-maximal monotonicity for nonlinear variational inclusionsRam U. Verma대한수학회 · 대한수학회논문집2011 · 제26권 제4호Iterative Algorithm for a New System of Variational Inclusions with B-monotone Operators in Banach Spaces이상근, 정재욱경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제3호

이 간행물의 다른 논문 (10건)

Slightly Fuzzy Continuous mappingsM. K. Uma, E. Roja, M. Sudhapp. 119-126Subordination Results for Certain Classes of Multivalently Analytic Functions with a Convolution StructureR. K. Raina, J. K. Prajapatpp. 127-140On generalized nonlinear quasivariational inequalitiesJinsong Li, 강신민pp. 141-146An Improved Newton-Kantorovich Theorem and Interior Point MethodsIoannis K. Argyrospp. 147-151Convergence of the Newton Method for Aubin Continuous MapsIoannis K. Argyrospp. 153-157
원문 보기