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Discrete optimization in partially ordered sets

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  • S. Basha

Abstract

The primary aim of this article is to resolve a global optimization problem in the setting of a partially ordered set that is equipped with a metric. Indeed, given non-empty subsets A and B of a partially ordered set that is endowed with a metric, and a non-self mapping $${S : A \longrightarrow B}$$ , this paper discusses the existence of an optimal approximate solution, designated as a best proximity point of the mapping S, to the equation Sx = x, where S is a proximally increasing, ordered proximal contraction. An algorithm for determining such an optimal approximate solution is furnished. Further, the result established in this paper realizes an interesting fixed point theorem in the setting of partially ordered set as a special case. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • S. Basha, 2012. "Discrete optimization in partially ordered sets," Journal of Global Optimization, Springer, vol. 54(3), pages 511-517, November.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:3:p:511-517
    DOI: 10.1007/s10898-011-9774-2
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    Cited by:

    1. Hussain, Nawab & Kutbi, M.A. & Salimi, Peyman, 2020. "Global optimal solutions for proximal fuzzy contractions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    2. Calogero Vetro & Peyman Salimi, 2013. "Best proximity point results in non-Archimedean fuzzy metric spaces," Fuzzy Information and Engineering, Springer, vol. 5(4), pages 417-429, December.

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