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

  • Supak Phiangsungnoen
  • Nopparat Wairojjana
  • Poom Kumam
Chapter

Abstract

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.

Keywords

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

Notes

Acknowledgments

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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