The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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GENERALIZED MULTIVALUED QUASIVARIATIONAL INCLUSIONS FOR FUZZY MAPPINGS

  • Liu, Zeqing (DEPARTMENT OF MATHEMATICS, LIAONING NORMAL UNIVERSITY) ;
  • Ume, Jeong-Sheok (DEPARTMENT OF APPLIED MATHEMATICS, CHANGWON NATIONAL UNIVERSITY) ;
  • Kang, Shin-Min (DEPARTMENT OF MATHEMATICS AND RESEARCH INSTITUTE OF NATURAL SCIENCE, GYEONGSANG NATIONAL UNIVERSITY)
  • Published : 2007.02.28
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Abstract

In this paper, we introduce and study a class of generalized multivalued quasivariational inclusions for fuzzy mappings, and establish its equivalence with a class of fuzzy fixed-point problems by using the resolvent operator technique. We suggest a new iterative algorithm for the generalized multivalued quasivariational inclusions. Further, we establish a few existence results of solutions for the generalized multivalued quasivariational inclusions involving $F_r$-relaxed Lipschitz and $F_r$-strongly monotone mappings, and discuss the convergence criteria for the algorithm.

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