A best proximity point theorem for Geraghty-contractions

Research

J Caballero, J Harjani and K Sadarangani^*

Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, Las Palmas de Gran Canaria, 35017, Spain

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Fixed Point Theory and Applications 2012, 2012:231 doi:10.1186/1687-1812-2012-231

Published: 27 December 2012

The purpose of this paper is to provide sufficient conditions for the existence of a unique best proximity point for Geraghty-contractions.

Our paper provides an extension of a result due to Geraghty (Proc. Am. Math. Soc. 40:604-608, 1973).

fixed point; Geraghty-contraction; P-property; best proximity point