Selecting families and their applications

  • Authors:

  • M. Balaj;Lai-Jiu Lin

  • Affiliations:

  • Department of Mathematics, University of Oradea, 410087 Oradea, Romania;Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2008

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Abstract

Deguire and Lassonde [P. Deguire, M. Lassonde, Familles selectantes, Topol. Methods Nonlinear Anal. 5 (1995) 261-269] extend the concept of continuous selection and introduce the notion of selecting family for a family of set-valued mappings. In this paper, we first establish a new existence theorem of selecting families. The existence of the selecting families will be then used in order to obtain several fixed component theorems of Fan-Browder type, an intersection result, a maximal element theorem for a family of set-valued mappings and a minimax inequality.