Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas

, Volume 108, Issue 2, pp 369–375

Common \(f\)-endpoint for hybrid generalized multi-valued contraction mappings

Original Paper

DOI: 10.1007/s13398-012-0107-1

Cite this article as:
Abbas, M. & Khojasteh, F. RACSAM (2014) 108: 369. doi:10.1007/s13398-012-0107-1


In this paper, we introduce common approximate \(f\)-endpoint property for multi-valued mapping \(T:X\rightarrow P_{cl,bd}(X)\) to obtain a necessary and sufficient condition for existence of a unique common \(f\)-endpoint for such multi-valued mappings. Our results extend and unify comparable results in existing literature (see for example, Kamran in Nonlinear Anal (TMA) 67:2289–2296, 2007; Sintunavarat and Kumam in Appl Math Lett 25:52–57, 2012 and references mentioned therein). We also provide an example to support our results.


Multi-valued mappingApproximate \(f\)-endpoint property Common endpointHybrid generalized contraction Hausdorff metric

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  1. 1.The University of Birmingham School of MathematicsBirminghamUK
  2. 2.Department of MathematicsLahore University of Management SciencesLahorePakistan
  3. 3.Department of MathematicsIslamic Azad UniversityArakIran