Best Proximity Points for Some Classes of Proximal Contractions

Maryam A. Alghamdi, Naseer Shahzad and Francesca Vetro

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: Given a self‐mapping g : A → A and a non‐self‐mapping T : A → B, the aim of this work is to provide sufficient conditions for the existence of a unique point x ∈ A, called g‐best proximity point, which satisfies d(gx, Tx) = d(A, B). In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function x → d(gx, Tx), thereby getting an optimal approximate solution to the equation Tx = gx. An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach′s contraction principle to the case of non‐self‐mappings.

Date: 2013
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https://doi.org/10.1155/2013/713252

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:713252

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