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)
Liu, Zeqing,
Ume, Jeong-Sheok,
&
Kang, Shin-Min.
(2007). GENERALIZED MULTIVALUED QUASIVARIATIONAL INCLUSIONS FOR FUZZY MAPPINGS. , 14(1), 37-48.
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
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fuzzy mapping,
generalized multivalued quasivariational inclusions,
iterative algorithm