Journal of Convex Analysis 24 (2017), No. 1, 041--053
Copyright Heldermann Verlag 2017
A Best Proximity Point Theorem Using Discontinuous Functions
Binayak S. Choudhury
Dept. of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O.B. Garden, Howrah - 711103, West Bengal, India
binayak12@yahoo.co.in
Pranati Maity
Dept. of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O.B. Garden, Howrah - 711103, West Bengal, India
pranati.math@gmail.com
Kishin Sadarangani
Dep. de Matemáticas, Universidad de Las Palmas, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain
ksadaran@dma.ulpgc.es
We prove a best proximity point theorem for generalized weak contractions with discontinuous control functions in the context of metric spaces and partially ordered metric spaces. The main argument in our proofs is based on transforming a question of best proximity point to one about a fixed point. Moreover, we will use a weaker condition than the P-property and we present two examples to illustrate our results.
Keywords: Non-self map, weak P-property, best proximity point, control function, weak contraction.
MSC: 54H25, 47H10
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