Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

ITERATIVE ALGORITHM FOR COMPLETELY GENERALIZED QUASI-VARIATIONAL INCLUSIONS WITH FUZZY MAPPINGS IN HILBERT SPACES

  • 발행 : 2010.01.30
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초록

In this paper, we introduce and study a class of completely generalized quasi-variational inclusions with fuzzy mappings. A new iterative algorithm for finding the approximate solutions and the convergence criteria of the iterative sequences generated by the algorithm are also given. These results of existence, algorithm and convergence generalize many known results.

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참고문헌

  1. S. Adly, Perturbed algorithms and sensitivity analysis for a general class of variational inclisions, J. Math. Anal. Appl. 201(3)(1996), 609-630.
  2. S. S. Chang and Y. G. Zhu, On variational inequalities for fuzzy mappings, Fuzzy Sets and Systems, 32(1989), 359-376. https://doi.org/10.1016/0165-0114(89)90268-6
  3. S. S. Chang and N. J. Huang, Generalized complementarity problem for fuzzy mappings, Fuzzy Sets and Systems, 55(2)(1993), 227-234. https://doi.org/10.1016/0165-0114(93)90135-5
  4. X. P. Ding, Perturbed proximal point algorithm for generalized quasivariational inclusions, J. Math. Anal. Appl. 210(1997), 88-101. https://doi.org/10.1006/jmaa.1997.5370
  5. X. P. Ding, Algorithms of solutions for completely generalized mixed implicit quasivariational inclusions, Appl. Math. Comput. 148(2004), 47-66. https://doi.org/10.1016/S0096-3003(02)00825-1
  6. A. Hassouni and A. Moudafi, it perturbed algorithm for variational inclusions, J. Math. Anal. Appl. 185(3)(1994), 706-712. https://doi.org/10.1006/jmaa.1994.1277
  7. H. J. Huang, Generalized nonlinear variational inclusions with noncompact valued mappings, Appl. Math. Lett. 9(3)(1996), 25-27. https://doi.org/10.1016/0893-9659(96)00026-2
  8. H. J. Huang, A new method for a class of nonlinear variational inequalities with fiuzzy mappings, Appl. Math. Lett. 10(6)(1997), 129-133. https://doi.org/10.1016/S0893-9659(97)00116-X
  9. K. R. Kazmi, Ishikawa perturbed iterative algorithms for generalized quasi-variational inclusions, J. Math. Anal. Appl. 210(1)(1997), 88-101. https://doi.org/10.1006/jmaa.1997.5370
  10. S. B. Nadler, Jr., Multivalued contraction mappings, Pacific J. Math. 30(1969), 475-488. https://doi.org/10.2140/pjm.1969.30.475
  11. M. A. Noor, Variational inequalities for fuzzy mappings (I), Fuzzy Sets and Systems, 55(1993), 309-312. https://doi.org/10.1016/0165-0114(93)90257-I
  12. J. Y. Park and J. U. Jeong, Strongly variational inequalities for fuzzy mappings, The Journal of Fuzzy Mathematics, 6(2)(1998), 475-482.
  13. J. Y. Park and J. U. Jeong, Generalized strongly quasivariational inequalities for fuzzy mappings, Fuzzy Sets and Systems, 99(1998), 115-120. https://doi.org/10.1016/S0165-0114(97)00027-4
  14. J. Y. Park and J. U. Jeong, A perturbed algorithm of variational inclusions for fuzzy mappings, Fuzzy Sets and Systems, 115(2000), 419-424. https://doi.org/10.1016/S0165-0114(99)00116-5
  15. J. Y. Park and J. U. Jeong, Iterative algorithm for finding approximate solutions to completely generalized strongly quasivariational inequalities for fuzzy mappings, Fuzzy Sets and Systems, 115(2000), 413-418. https://doi.org/10.1016/S0165-0114(98)00339-X
  16. J. Y. Park, S. Y. Lee and J. U. Jeong, Completely generalized strongly quasivariational inequalities for fuzzy mappings, Fuzzy Sets and Systems, 110(2000), 91-99. https://doi.org/10.1016/S0165-0114(98)00106-7
  17. J. Y. Park and J. U. Jeong, Mixed quasivariational inequalities with fuzzy mappings, The Journal of Fuzzy Mathematics, 10(4)(2002), 901-912.
  18. D. Pascali and S. Sburlan, Nonlinear Mappings of Monotone Type, Sijthoff and Noordhoof Intern. Pub., The Netherlands, 1978.