Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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COINCIDENCE THEOREMS FOR NONCOMPACT ℜℭ-MAPS IN ABSTRACT CONVEX SPACES WITH APPLICATIONS

  • Received : 2009.06.01
  • Published : 2012.11.30
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Abstract

In this paper, a coincidence theorem for a compact ${\Re}\mathfrak{C}$-map is proved in an abstract convex space. Several more general coincidence theorems for noncompact ${\Re}\mathfrak{C}$-maps are derived in abstract convex spaces. Some examples are given to illustrate our coincidence theorems. As applications, an alternative theorem concerning the existence of maximal elements, an alternative theorem concerning equilibrium problems and a minimax inequality for three functions are proved in abstract convex spaces.

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