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Efficacy of cones on topological vector spaces and application to common fixed points of multifunctions

Abstract

Let (E, τ) be a topological vector space and P a cone in E. We shall define a topology τ P on E so that (E, τ P ) is a normable topological vector space and P is a normal cone with normal constant M = 1. Then by using the norm, we shall give some results about common fixed points of two multifunctions on cone metric spaces.

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Correspondence to Shahram Rezapour.

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Rezapour, S., Khandani, H. & Vaezpour, S.M. Efficacy of cones on topological vector spaces and application to common fixed points of multifunctions. Rend. Circ. Mat. Palermo 59, 185–197 (2010). https://doi.org/10.1007/s12215-010-0014-2

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  • DOI: https://doi.org/10.1007/s12215-010-0014-2

Keywords

  • Common fixed point
  • Multifunction
  • Non-normal cone
  • Topological vector space

Mathematics Subject Classification (2000)

  • 47H10
  • 54H25