\(q^\lambda \)-hyperconvexity in quasi-metric spaces

  • Collins Amburo AgyingiEmail author
  • Yaé Ulrich Gaba


In this article, we introduce and study the concept of hyperconvexity (which we call \(q^\lambda \)-hyperconvexity) that is appropriate in the category of \(T_0\)-quasi-metric spaces and nonexpansive maps and this will generalize the notion of q-hyperconvexity studied by Kemajou et al. We prove a fixed point result for nonexpansive maps in \(q^\lambda \)-hyperconvex spaces and establish, among other things, that the fixed point set of nonexpansive maps on \(q^\lambda \)-hyperconvex bounded \(T_0\)-quasi-metric spaces is itself \(q^\lambda \)-hyperconvex.


q-hyperconvexity \(q^\lambda \)-hyperconvexity Isbell-convex Isbell-complete Nonexpansive maps 

Mathematics Subject Classification

Primary 54X10 58Y30 18D35 Secondary 55Z10 



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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Applied MathematicsNelson Mandela UniversityPort ElizabethSouth Africa
  2. 2.Institut de Mathématiques et de Sciences Physiques (IMSP)/UACPorto-NovoBenin
  3. 3.African Center for Advanced Studies (ACAS)YaoundéCameroon

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