Best proximity points for some classes of proximal contractions

Francesca Vetro, Maryam A. Alghamdi, Naseer Shahzad

    Risultato della ricerca: Articlepeer review

    15 Citazioni (Scopus)

    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.
    Lingua originaleEnglish
    pagine (da-a)1-10
    Numero di pagine0
    RivistaAbstract and Applied Analysis
    Volume2013
    Stato di pubblicazionePublished - 2013

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Applied Mathematics

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