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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

GENERALIZED MULTIVALUED QUASIVARIATIONAL INCLUSIONS FOR FUZZY MAPPINGS

Generalized Multivalued Quasivariational Inclusions for Fuzzy Mappings

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2007, v.14 no.1, pp.37-48
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)

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 <TEX>$F_r$</TEX>-relaxed Lipschitz and <TEX>$F_r$</TEX>-strongly monotone mappings, and discuss the convergence criteria for the algorithm.

keywords
fuzzy mapping, generalized multivalued quasivariational inclusions, iterative algorithm

한국수학교육학회지시리즈B:순수및응용수학