Existence and convergence results for best proximity points in cone metric spaces
This paper is an attempt to extend the best proximity results of \textit{S. S. Basha} [Optim. Lett. 7, No. 6, 1167--1177 (2013; Zbl 1298.90075)] to the framework of cone metric spaces in the sense of \textit{L.-G. Huang} and \textit{X. Zhang} [J. Math. Anal. Appl. 332, No. 2, 1468--1476 (2007; Zbl 1118.54022)]. However, several places remain unclear. E.g., what is the distance \(d(A,B)\) of sets in a cone metric space? What is the norm \(\|S\|\) of an operator in a cone metric space? In Theorem 3.5, what is the connection of \(x^*\) with the constructed sequences \(\{x_n\}\) and \(\{y_n\}\)? Etc. Moreover, only trivial examples are given, with orderings which are total, so the need of considering more general orders is not justified.
generalized cone proximal \(\phi\)-cyclic contraction pairs
scientific article; zbMATH DE number 6376984