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

Document Type : Original Article

Authors
Moosa Gabeleh 1
Jack Markin 2
1 Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.
2 1440 8th St. Golden, Co 80401, USA; jmarkin@newmexico.com
10.22034/maco.2.1.7
Abstract
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, 63 (2014), 817-825}] 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. 7 (2013), 1883–1892}] the results are not real generalizations but particular cases of existing fixed point theorems in the literature. 

Keywords

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Mathematical Analysis and Convex Optimization
Volume 2, Issue 1
June 2021
Pages 71-78