Acta Mathematica Hungarica

, Volume 157, Issue 1, pp 173–190 | Cite as

Min-max property in metric spaces with convex structure

  • M. GabelehEmail author
  • H.-P. A. Künzi


In the setting of convex metric spaces, we introduce the two geometric notions of uniform convexity in every direction as well as sequential convexity. They are used to study a concept of proximal normal structure. We also consider the class of noncyclic relatively nonexpansive mappings and analyze the min-max property for such mappings. As an application of our main results we conclude with some best proximity pair theorems for noncyclic mappings.

Key words and phrases

proximal normal structure noncyclic relatively nonexpansive mapping uniformly in every direction convex metric space 

Mathematics Subject Classification

54E35 47H09 46B20 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Ayatollah Boroujerdi UniversityBoroujerd, School of Mathematics, Institute for Research in Fundamental Sciences (IPM)TehranIran
  2. 2.Department of Mathematics and Applied MathematicsUniversity of Cape TownRondeboschSouth Africa

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