Best proximity points: approximation and optimization
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- Sadiq Basha, S., Shahzad, N. & Jeyaraj, R. Optim Lett (2013) 7: 145. doi:10.1007/s11590-011-0404-1
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A best proximity point theorem explores the existence of an optimal approximate solution, known as a best proximity point, to the equations of the form Tx = x where T is a non-self mapping. The purpose of this article is to establish some best proximity point theorems for non-self non-expansive mappings, non-self Kannan- type mappings and non-self Chatterjea-type mappings, thereby producing optimal approximate solutions to some fixed point equations. Also, algorithms for determining such optimal approximate solutions are furnished in some cases.