A note on ‘A best proximity point theorem for Geraghty-contractions’

Author:

Zhang Jingling,Su Yongfu,Cheng Qingqing

Abstract

Abstract In Caballero et al. (Fixed Point Theory Appl. (2012). doi:10.1186/1687-1812-2012-231), the authors prove a best proximity point theorem for Geraghty nonself contraction. In this note, not only P-property has been weakened, but also an improved best proximity point theorem will be presented by a short and simple proof. An example which satisfies weak P-property but not P-property has been presented to demonstrate our results. MSC:47H05, 47H09, 47H10.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Geometry and Topology

Reference4 articles.

1. Geraghty M: On contractive mappings. Proc. Am. Math. Soc. 1973, 40: 604–608. 10.1090/S0002-9939-1973-0334176-5

2. Caballero J, et al.: A best proximity point theorem for Geraghty-contractions. Fixed Point Theory Appl. 2012. doi:10.1186/1687–1812–2012–231

3. Kirk WA, Reich S, Veeramani P: Proximinal retracts and best proximity pair theorems. Numer. Funct. Anal. Optim. 2003, 24: 851–862. 10.1081/NFA-120026380

4. Sankar Raj, V: Banach contraction principle for non-self mappings. Preprint

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