Pythagorean Property and Best-Proximity Point Theorems

Rafael Espínola (), G. Sankara Raju Kosuru () and P. Veeramani ()
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Rafael Espínola: IMUS, Universidad de Sevilla
G. Sankara Raju Kosuru: Indian Statistical Institute Bangalore
P. Veeramani: Indian Institute of Technology Madras

Journal of Optimization Theory and Applications, 2015, vol. 164, issue 2, No 8, 534-550

Abstract: Abstract In this paper, a notion called proximally complete pair of subsets of a metric space is introduced, which weakens earlier notions in the theory of best-proximity points. By means of this notion, existence and convergence results of best-proximity points are proven for cyclic contraction mappings, which extent other recent results. By observing geometrical properties of Hilbert spaces, the so-called Pythagorean property is introduced. This property is employed to provide sufficient conditions for a cyclic map to be a cyclic contraction.

Keywords: Cyclic contraction; Sharp proximinal pair; Proximal complete pair; Best-proximity points; Pythagorean property; 47H10; 46C20; 54H25 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-014-0583-x

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