Date: 02 Nov 2012

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

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Abstract

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.