• Title/Summary/Keyword: better admissible class of multimaps

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HOMOTOPY RESULTS FOR THE BETTER ADMISSIBLE CHANDRABHAN TYPE MULTIMAPS

  • Kim, Hoonjoo
    • Journal of the Chungcheong Mathematical Society
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    • v.35 no.4
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    • pp.297-305
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    • 2022
  • First, we generalize homotopy results of O'Regan [6] for Mönch type multimaps to Chandrabhan type multimaps. Second, we show that the better admissible Chandrabhan type multimaps have fixed point properties whenever their ranges are Klee approximable. Finally, we give examples of essential maps for various class of multimaps including 𝚽-condensing multimaps.

FIXED POINTS OF BETTER ADMISSIBLE MAPS ON GENERALIZED CONVEX SPACES

  • Park, Se-Hie
    • Journal of the Korean Mathematical Society
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    • v.37 no.6
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    • pp.885-899
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    • 2000
  • We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

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FIXED POINT THEOREMS FOR MӦNCH TYPE MAPS IN ABSTRACT CONVEX UNIFORM SPACES

  • Kim, Hoonjoo
    • Journal of the Chungcheong Mathematical Society
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    • v.34 no.4
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    • pp.345-353
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    • 2021
  • In this paper, first, we present new fixed point theorems for Mönch type multimaps on abstract convex uniform spaces and, also, a fixed point theorem for Mönch type multimaps in Hausdorff KKM L𝚪-spaces. Second, we show that Mönch type multimaps in the better admissible class defined on an L𝚪-space have fixed point properties whenever their ranges are Klee approximable. Finally, we obtain fixed point theorems on 𝔎ℭ-maps whose ranges are 𝚽-sets.

RECENT RESULTS AND CONJECTURES IN ANALYTICAL FIXED POINT THEORY

  • Park, Se-Hie
    • East Asian mathematical journal
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    • v.24 no.1
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    • pp.11-20
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    • 2008
  • We survey recent results and some conjectures in analytical fixed point theory. We list the known fixed point theorems for Kakutani maps, Fan-Browder maps, locally selectionable maps, approximable maps, admissible maps, and the better admissible class $\cal{B}$ of maps. We also give 16 conjectures related to that theory.

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A UNIFIED FIXED POINT THEORY OF MULTIMAPS ON TOPOLOGICAL VECTOR SPACES

  • Park, Seh-Ie
    • Journal of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.803-829
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    • 1998
  • We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

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COLLECTIVE FIXED POINTS FOR GENERALIZED CONDENSING MAPS IN ABSTRACT CONVEX UNIFORM SPACES

  • Kim, Hoonjoo
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.1
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    • pp.93-104
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    • 2021
  • In this paper, we present a fixed point theorem for a family of generalized condensing multimaps which have ranges of the Zima-Hadžić type in Hausdorff KKM uniform spaces. It extends Himmelberg et al. type fixed point theorem. As applications, we obtain some new collective fixed point theorems for various type generalized condensing multimaps in abstract convex uniform spaces.