Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Non-self map
  • weak P-property
  • best proximity point
  • control function
  • weak contraction

Mathematics Subject Classification

54H25, 47H10

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Suggested citation

B. S. Choudhury, P. Maity, K. Sadarangani. “A Best Proximity Point Theorem Using Discontinuous Functions.” Journal of Convex Analysis 24 (2017), No. 1, 41–53. https://doi.org/10.68381/jca24003

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.