• 제목/요약/키워드: multifunctions

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On Upper and Lower Z-supercontinuous Multifunctions

  • Akdag, Metin
    • Kyungpook Mathematical Journal
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    • v.45 no.2
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    • pp.221-230
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    • 2005
  • In this paper, we define a multifunction $F:X{\rightarrow}Y$ to be upper (lower) Z -supercontinuous if $F^{+}(V)(F^{-}(V))$ is z-open in X for every open set V of Y. We obtain some characterizations and several properties concerning upper (lower) Z-supercontinuous multifunctions.

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ON UPPER AND LOWER SEMI-IRRESOLUTE FUZZY MULTIFUNCTIONS

  • Seenivasan, V.;Balasubramanian, G.
    • East Asian mathematical journal
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    • v.23 no.1
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    • pp.9-22
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    • 2007
  • New classes of multifunctions called fuzzy upper and fuzzy lower semi-irresolute (semi-continuous) multifunctions in fuzzy topological spaces are introduced in this paper. We also obtain some characterizations of this class and some basic interesting properties of such fuzzy multifunctions. We discuss mutual relationship and also relationship with other existing such multifunctions.

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GENERALIZED VARIATIONAL-LIKE INEQUALITIES WITH COMPOSITELY MONOTONE MULTIFUNCTIONS

  • Ceng, Lu-Chuan;Lee, Gue-Myung;Yao, Jen-Chih
    • Journal of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.841-858
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    • 2008
  • In this paper, we introduce two classes of generalized variational-like inequalities with compositely monotone multifunctions in Banach spaces. Using the KKM-Fan lemma and the Nadler's result, we prove the existence of solutions for generalized variational-like inequalities with compositely relaxed ${\eta}-{\alpha}$ monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the solvability of generalized variational-like inequalities with compositely relaxed ${\eta}-{\alpha}$ semimonotone multi functions in arbitrary Banach spaces by virtue of the Kakutani-Fan-Glicksberg fixed-point theorem. The results presented in this paper extend and improve some earlier and recent results in the literature.

FIXED POINT OF α - ψ - CONTRACTIVE MULTIFUNCTION IN FUZZY METRIC SPACES

  • KUMAR, MOHIT;ARORA, RIITU
    • Journal of applied mathematics & informatics
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    • v.35 no.3_4
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    • pp.323-330
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    • 2017
  • Recently Samet, Vetro and Vetro introduced the notion of ${\alpha}$-${\Psi}$-contractive type mappings and initiated some fixed point theorems in complete metric spaces. The notion of ${\alpha}_*$ - ${\Psi}$-contractive multifunctions and initiated some fixed point results by Hasanzade Asl et. al. [8]. In this paper, we introduced the notion of ${\alpha}_*$ - ${\Psi}$-contractive multifunctions in a fuzzy metric space and gave fixed point results for these multifunctions in complete fuzzy metric spaces. We also obtain a fixed point results for self-maps in complete fuzzy metric spaces satisfying contractive condition.

ON SOME TYPES OF CONTINUOUS FUZZY MULTIFUNCTIONS

  • Ekici, Erdal
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.4
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    • pp.647-656
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    • 2004
  • In this paper, by using operations, some characterizations and some properties of fuzzy lower and upper continuous multifunctions and its weaker and stronger forms including fuzzy lower and upper weakly continuous, fuzzy lower and upper ${\theta}-continuous$, fuzzy lower and upper strongly ${\theta}-continuous$, fuzzy lower and upper almost strongly ${\theta}-continuous$, fuzzy lower and upper weakly ${\theta}-continuous$, fuzzy lower and upper almost continuous, fuzzy lower and upper super continuous, fuzzy lower and upper ${\delta}-continuous$, are presented.

SENSITIVITY ANALYSIS FOR A CLASS OF IMPLICIT MULTIFUNCTIONS WITH APPLICATIONS

  • Li, Shengjie;Li, Minghua
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.2
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    • pp.249-262
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    • 2012
  • In this paper, under some suitable conditions and in virtue of a selection which depends on a vector-valued function and a feasible set map, the sensitivity analysis of a class of implicit multifunctions is investigated. Moreover, by using the results established, the solution sets of parametric vector optimization problems are studied.