Given a self-mapping g: A → A and a non-self-mapping T: A → B, the aim of this work is to provide sufficient conditions for the existence of a unique point x ∈ A, called g-best proximity point, which satisfies d g x, T x = d A, B. In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function x → d g x, T x, thereby getting an optimal approximate solution to the equation T x = g x. An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-self-mappings. © 2013 Maryam A. Alghamdi et al.

Alghamdi, M.A., Shahzad, N., Vetro, F. (2013). Best proximity points for some classes of proximal contractions. ABSTRACT AND APPLIED ANALYSIS, 2013, 1-10 [10.1155/2013/713252].

Best proximity points for some classes of proximal contractions

VETRO, Francesca
2013-01-01

Abstract

Given a self-mapping g: A → A and a non-self-mapping T: A → B, the aim of this work is to provide sufficient conditions for the existence of a unique point x ∈ A, called g-best proximity point, which satisfies d g x, T x = d A, B. In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function x → d g x, T x, thereby getting an optimal approximate solution to the equation T x = g x. An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-self-mappings. © 2013 Maryam A. Alghamdi et al.
2013
Settore MAT/03 - Geometria
Alghamdi, M.A., Shahzad, N., Vetro, F. (2013). Best proximity points for some classes of proximal contractions. ABSTRACT AND APPLIED ANALYSIS, 2013, 1-10 [10.1155/2013/713252].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/91585
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