Some Remarks on The Paper "Global Optimization in Metric Spaces With Partial Orders"

The aim of this note is to show that the main conclusion of a recent paper by Sadiq Basha [S. Sadiq Basha, Global optimization in metric spaces with partial orders, emph{Optimization, ۶۳ (۲۰۱۴), ۸۱۷-۸۲۵}] can be obtained as a consequence of corresponding existing results in fixed point theory in the setting of partially ordered metric spaces. Moreover, by a similar approach, we prove that in the paper [V. Pragadeeswarar, M. Marudai, Best proximity points: approximation and optimization in partially ordered metric spaces, emph{Optim. Lett. ۷ (۲۰۱۳), ۱۸۸۳–۱۸۹۲}] the results are not real generalizations but particular cases of existing fixed point theorems in the literature.

Keywords:

partially ordered set , proximally increasing mapping , ordered proximal contraction , best proximity point