Fixed Point Theorem and Stability for (α, ψ, ξ)-Generalized Contractive Multivalued Mappings

  • Supak Phiangsungnoen
  • Nopparat Wairojjana
  • Poom Kumam


In this paper, we introduce and prove a fixed point theorem for \( (\alpha ,\psi ,\xi ) \)-generalized contractive multivalued mappings on collections of non-empty closed subsets. We also prove the \( \xi \)-generalized Ulam-Hyers stability results for fixed point inclusion. Finally, we provide illustrative example to support our main result.


Admissible mapping \( (\alpha ,\psi ,\xi ) \)-generalized contractive Fixed point Generalized Ulam-Hyer stability Hausdorff metric Multivalued mappings 



The authors were supported by the Higher Education Research Promotion and National Research University Project of Thailand, Office of the Higher Education Commission (NRU-CSEC No.55000613).


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Supak Phiangsungnoen
    • 1
  • Nopparat Wairojjana
    • 2
  • Poom Kumam
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceKing Mongkut’s University of Technology Thonburi (KMUTT)Thung KhruThailand
  2. 2.Faculty of Science and TechnologyValaya Alongkorn Rajabhat University under the Royal PatronageKlong Luang DistrictThailand

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