Original Paper

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

, Volume 108, Issue 2, pp 369-375

First online:

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

  • Mujahid AbbasAffiliated withThe University of Birmingham School of MathematicsDepartment of Mathematics, Lahore University of Management Sciences
  • , Farshid KhojastehAffiliated withDepartment of Mathematics, Islamic Azad University Email author 

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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 mapping Approximate \(f\)-endpoint property Common endpoint Hybrid generalized contraction Hausdorff metric

Mathematics Subject Classification (2000)

47H10 54C60