본문 바로가기
KERD
논문KCI 등재

Strong convergence of an iterative algorithm for a class of nonlinear set-valued variational inclusions

2

조회

0

다운로드

2

인용

0

참고문헌

키워드

주제분류수학

초록

In this communication, we introduce an Ishikawa type iterative algorithm for finding the approximate solutions of a class of nonlinear set valued variational inclusion problems. We also establish a characterization of strong convergence of this iterative techniques.

Abstract

In this communication, we introduce an Ishikawa type iterative algorithm for finding the approximate solutions of a class of nonlinear set valued variational inclusion problems. We also establish a characterization of strong convergence of this iterative techniques.

참고문헌 (41)

  1. D. Kinderlehrer, "An introduction to variational inequalities and their applications" (1980), Academic Press
  2. J. P. Aubin, "Mathematical methods of game theory and economics" (1982), North Holland
  3. H. Brezis, "Operateurs maximaux monotone er semi groupes de contractions dans les espaces de Hilbert" (1973), North-Holland
  4. R. E. Bruck, "Accretive operators, Banach limits and dual ergodic theorems", Bull. Acad. Polon Sci, 12, pp.585~589 (1981)
  5. R. Glowinski, "Numerical analysis of variational inequalities" (1981), North-Holland
  6. F. Giannessi, "Variational inequalities and network equilibrium problems" (1995), Plenum Press
  7. L. Gioranescu, "Geometry of Banach spaces, duality mapping and nonlinear prob-lems" (1990), kluwer Acad. Press
  8. N. Kikuchi, "Contact problems in elasticity" (1988), SIAM
  9. P. D. Panagiotoupoulos, "New types of variational princi-ples based on the notion of quasi di erentiability", Acta Mech, 94, pp.171~194 (1992)
  10. A. Hassouni, "A perturbed algorithms for variational inequalities", J. Math. Anal. Appl, 185, pp.706~712 (1994)
  11. X. P. Ding, "Perturbed proximal point algorithms for generalized quasi variational inclusions", J. Math. Appl. Appl, 201, pp.88~101 (1997)
  12. X. P. Ding, "Proximal point algorithm with errors for generalized strongly non-linear quasi-variational inclusions", Appl. Math. Mech, 19(7), pp.637~643 (1998)
  13. X. P. Ding, "On a class of generalized nonlinear implicit quasivariational inclu-sions", Appl. Math. Mech, 20(10), pp.1087~1098 (1999)
  14. X. P. Ding, "Generalized implicit quasivariational inclusions with fuzzy set-valued mappings", Comput. Math. Appl, 38(1), pp.71~79 (1999)
  15. X. P. Ding, "Perturbed proximal point algorithms for general quasi-variational-like inclusions", J. Computat. Appl. Math, 113, pp.153~165 (2000)
  16. X. P. Ding, "Generalized quasi-variational-like inclusions with nonconvex func-tionals", Appl. Math. Comput, 122, pp.267~282 (2001)
  17. X. P. Ding, "Perturbed Ishikawa Type Iterative Algorithm for Generalized Quasi-variational Inclusions", Appl. Math. Comput, 14, pp.359~373 (2003)
  18. X. P. Ding, "Algorithms of solutions for completely generalized mixed implicit quasivariational inclusions", Appl. Math. Comput, 148(1), pp.47~66 (2004)
  19. X. P. Ding, "Predictor-Corrector iterative algorithms for solving generalized mixed quasi-variational-like inclusion", J. Comput. Appl. Math, 182(1), pp.1~12 (2005)
  20. Wentang Wu, "Numerical investigation of turbulent channel flow controlled by spatially oscillating spanwise Lorentz force", Applied Mathematics and Mechanics, 36(9), pp.1113~1120 (2015), Springer Nature[DOI]
  21. X. P. Ding, "The p-step iterative algorithm for a system of gen-eralized mixed quasi-variational inclusions with (A; )-accretive operators in q-uniformly smooth Banach spaces", J. Comput. Appl. Math, 220(1-2), pp.163~174 (2008)
  22. 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)
  23. X. P. Ding, "Sensitivity analysis for a system of parametric gen-eralized mixed quasi-variational inclusions involving (K; )-monotone mappings", Appl. Math. Comput, 214, pp.318~327 (2009)
  24. X. P. Ding, "Auxiliary principle and algorithm for a system of gen-eralized set-valued mixed variational-like inequality problems in Banach spaces", J. Comput. Appl. Math, 223, pp.2876~2883 (2010)
  25. Y. P. Fang, "H-accretive operators and resolvent operators tech-nique for solving variational inclusions in Banach spaces", Appl. Math. Lett, 17(6), pp.647~653 (2004)
  26. X. He, "On -strongly accretive mapping and some set valued variational prob-lems", J. Math. Anal. Appl, 277(2), pp.504~511 (2003)
  27. N. J. Huang, "On the generalized implicit quasi variational inequalities", J. Math. Anal. Appl, 216, pp.197~210 (1997)
  28. J. S. Jung, "The Mann process for perturbed m-accretive op-erators in Banach spaces", Nonlinear Anal, 46(20), pp.231~243 (2001)
  29. S. S. Chang, "Set valued variational inclusions in Banach Spaces", J. Math. Anal. Appl, 248, pp.438~454 (2000)
  30. S. S. Chang, "On the existence and iterative approx-imation problems of solutions for set valued variational inclusions in Banach spaces", 268, pp.89~108 (2002)
  31. S. S. Chang, "Generalized set valued varia-tional inclusions in Banach spaces", J. Math. Anal. Appl, 246, pp.409~422 (2000)
  32. S. S. Chang, "A system of nonlinear set valued variational inclusions", SpringerPlus, 3, pp.318~ (2014)[DOI]
  33. S. S. Chang, "Iterative approxi-mations of xed points and solutions for strongly accretive and strongly pseudo contractive mappings in Banach Spaces", J. Math. Anal. Appl, 224, pp.149~165 (1998)
  34. L. C. Ceng, "On the characterization of strong convergence of an iterative algorithm for a class of multivalued variational in-clusions", Math. Math. Oper. Res, 70, pp.1~12 (2009)
  35. Y. J. Cho, "Approximations for xed points of -hemicontractive mappings by the Ishikawa iterative process with mixed errors", Math. Comput. Model, 34, pp.9~18 (2001)
  36. C. E. Chidume, "Existence and convergence theorem for a class of multivalued variational inclusions in Banach space", Nonlinear Anal, 59, pp.649~656 (2004)
  37. M. F. Khan, "Generalized multivalued nonlinear co-variational inequalities in Banach spaces", Funct. Diff. Equations, 14(2-4), pp.299~313 (2007)
  38. M. K. Ahmad, "Stable perturbed algorithms for a new class of generalized nonlinear implicit quasi variational inclusions in Banach spaces", Ad-vances in Pure Math, 2(2), pp.139~148 (2012)
  39. M. F. Khan, "Generalized co-complementarity problems in p-uniformly smooth Banach spaces", JIPAM, J. Inequal. Pure Appl. Math, 7(2), pp.11~ (2006)
  40. R. U. Verma, "Extended systems of nonlinear vector quasi vari-ational inclusions and extended systems of nonlinear vector quasi optimization problems in locally FC-spaces", Commun. Appl. Nonlinear Anal, 23(1), pp.71~88 (2016)
  41. Jr. S. B. Nadler, "Multivalued contraction mappings", Pacific J. Math, 30, pp.475~487 (1969)

관련 논문AI추천

이 간행물의 다른 논문 (9건)