Geodesic
A Best Proximity Point Theorem Using Discontinuous Functions
Journal of convex analysis, Tome 24 (2017) no. 1, pp. 41-53
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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.
Classification : 54H25, 47H10
Mots-clés : Non-self map, weak P-property, best proximity point, control function, weak contraction 
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     author = {B. S. Choudhury and P. Maity and K. Sadarangani},
     title = {A {Best} {Proximity} {Point} {Theorem} {Using} {Discontinuous} {Functions}},
     journal = {Journal of convex analysis},
     pages = {41--53},
     year = {2017},
     volume = {24},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a2/}
}
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B. S. Choudhury; P. Maity; K. Sadarangani. A Best Proximity Point Theorem Using Discontinuous Functions. Journal of convex analysis, Tome 24 (2017) no. 1, pp. 41-53. http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a2/