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Approximation Solvability for a System of Nonlinear Varia- tional Type Inclusions in Banach Spaces

Salahuddin
경북대학교 자연과학대학 수학과|2019.03|Kyungpook Mathematical Journal|제59권 제1호|pp. 101-123|DOI 10.5666/KMJ.2019.59.1.101

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키워드

algorithmsηiterative sequencesBanach spacessystem of nonlinear variational type inclusions(Hφ)-monotone operators
주제분류수학

초록

In this paper, we consider a system of nonlinear variational type inclusions involving (H,η,φ)-monotone operators in real Banach spaces. Further, we de ne a proximal operator associated with an (H,η,φ)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of theiterative sequences generated by the algorithms

Abstract

In this paper, we consider a system of nonlinear variational type inclusions involving (H,η,φ)-monotone operators in real Banach spaces. Further, we de ne a proximal operator associated with an (H,η,φ)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of theiterative sequences generated by the algorithms

참고문헌 (36)

  1. R. Ahmad, "Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear variational inclusions", Math. Comput. Appl, 6(1), pp.47~52 (2001)
  2. M. K. Ahmad, "Resolvent equation technique for generalized nonlinear variational inclusions", Adv. Nonlinear Var. Inequal, 5(1), pp.91~98 (2002)
  3. M. K. Ahmad, "Perturbed three step approximation process with errors for a generalized implicit nonlinear quasivariational inclusions", Int. J. Math. Math. Sci, pp.15~ (2006)
  4. M. K. Ahmad, "Generalized strongly nonlinear implicit quasivariational inequalities", J. Inequal. Appl, pp.16~ (2009)
  5. M. K. Ahmad, "A stable perturbed algorithms for a new class of generalized nonlinear implicit quasi variational inclusions in Banach spaces", Advances Pure Math, 2(2), pp.139~148 (2012)
  6. C. Baiocchi, "Variational and quasi variational inequalities: applications to free boundary problems" (1984), Wiley
  7. X. P. Ding, "Perturbed proximal point algorithms for generalized quasi variational inclusions", J. Math. Anal. Appl, 210, pp.88~101 (1997)
  8. X. P. Ding, "The p-step iterative algorithm for a system of generalized mixed quasi variational inclusions with (A, η)-accretive operators in q-uniformly smooth Banach spaces", J. Comput. Appl. Math., 220, pp.163~174 (2008)
  9. X. P. Ding, "Algorithm for solving a new class of generalized nonlinear implicit quasi variational inclusions in Banach spaces", Appl. Math. Comput, 208, pp.547~555 (2009)
  10. X. P. Ding, "A system of general nonlinear variational inclusions in Banach spaces", Appl. Math. Mech, 36(12), pp.1663~1167 (2015)
  11. Xie-Ping Ding, "Strong convergence of an iterative algorithm for a class of nonlinear set-valued variational inclusions", 한국수학논문집, 25(1), pp.19~35 (2017), 강원경기수학회[DOI]
  12. Approximate solutions for nonlinear operator inclusions with (H, η)-monotone operators, "Y. P. Fang", Sichuan Univ, ~ (2003)
  13. Y. P. Fang, "H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces", Appl. Math. Lett, 17(6), pp.647~653 (2004)
  14. Y. P. Fang, "Iterative algorithm for a system of variational inclusions involving H-accretive operators in Banach spaces", Acta Math. Hungar, 108(3), pp.183~195 (2005)
  15. 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)
  16. H. R. Feng, "A new system of generalized nonlinear quasi variational like inclusions with A-monotone operators in Banach spaces", J. Comput. Appl. Math, 225, pp.365~373 (2009)
  17. A. Hassouni, "A perturbed algorithm for variational inclusions", J. Math. Anal. Appl, 185(3), pp.706~712 (1994)
  18. X. F. He, "Iterative methods for solving variational inclusions in Banach spaces", J. Comput. Appl. Math, 203, pp.80~86 (2007)
  19. N. J. Huang, "Generalized m-accretive mappings in Banach spaces", J. Sichuan Univ, 38(4), pp.591~592 (2001)
  20. H. Hussain, "Mann and Ishikawa type perturbed iterative algorithms for completely generalized nonlinear variational Inclusions", Int. J. Math. Anal, 3(1), pp.51~62 (2006)
  21. P. Junlouchai, "On a new system of nonlinear regularized nonconvex variational inequalities in Hilbert spaces", J. Nonlinear Anal. Optim, 7(1), pp.103~115 (2016)
  22. M. F. Khan, "Generalized mixed multivalued variational inclusions involving H-accretive operators", Adv. Nonlinear Var. Inequal, 9(2), pp.29~47 (2006)
  23. M. F. Khan, "Generalized co-complementarity problems in p-uniformly smooth Banach spaces", JIPAM. J. Inequal. Pure Appl. Math., 7(2), pp.11~ (2006)
  24. M. F. Khan, "Generalized multivalued nonlinear co-variational inequalities in Banach spaces", Funct. Diff. Equ, 14(2-4), pp.299~313 (2007)
  25. S. H. Kim, "Fuzzy variational inclusions with (H, Φ, Ψ)-η-Monotone mappings in Banach Spaces", J. Adv. Res. Appl. Math, 4(1), pp.10~22 (2012)
  26. B. S. Lee, "Generalized nonlinear quasi variational inclusions in Banach spaces", Comput. Math. Appl, 56(5), pp.1414~1422 (2008)
  27. Byung-Soo Lee, "Hybrid-type set--valued variational--like inequalities in reflexive Banach spaces", Journal of Applied Mathematics and Informatics, 27(5), pp.1371~1379 (2009), 한국전산응용수학회
  28. X. P. Luo, "(H, Φ)-η-monotone operators in Banach spaces with an application to variational inclusions", Appl. Math. Comput, 216, pp.1131~1139 (2010)
  29. Jr. S. B. Nadler, "Multi valued contraction mappings", Pacific J. Math, 30, pp.475~488 (1969)
  30. J. W. Peng., "A system of variational inclusions with p-η-accretive operators", J. Comput. Appl. Math, 216, pp.198~209 (2008)
  31. Salahuddin, "Proximal methods for generalized nonlinear quasivariational inclusions", Math. Computat. Appl, 9(2), pp.165~171 (2004)
  32. S. Q. Shan, "A new system of generalized implicit setvalued variational inclusions in Banach spaces", Nonlinear Funct. Anal. Appl, 22(5), pp.1091~1105 (2017)
  33. A. H. Siddiqi, "Existence results for generalized nonlinear variational inclusions", Appl. Maths. Letts, 18(8), pp.859~864 (2005)
  34. Y. K. Tang, "A system of nonlinear set valued variational inclusions", SpringerPlus, 3(318) (2014)[DOI]
  35. R. U. Verma, "Fuzzy generalized complementarity problems in Banach spaces", PanAmer. Math. J, 17(4), pp.71~80 (2007)
  36. F. Q. Xia, "Variational inclusions with a general H-monotone operator in Banach spaces", Comput. Math. Appl, 54, pp.24~30 (2007)

관련 논문AI추천

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