Abstract
Abstract The main aim of this paper is to advise researchers in the field of Fixed Point Theory against an extended mistake that can be found in some proofs. We illustrate our claim proving that theorems in the very recent paper (Wang in Fixed Point Theory Appl. 2014:137, 2014) are incorrect, and we provide different corrected versions of them.
Highlights
Introduction and preliminariesLet (X, d) be a metric space, let k be a positive integer number, and let Xk = X × X × ·(k·)· × X be the Cartesian product of k identical copies of X
Theorem (Wang [, Theorem . ]) Let (X, ) be a partially ordered set and suppose that there is a metric d on X such that (X, d) is a complete metric space
4 A suggestion to correct Wang’s paper inspired by Wang’s paper [ ], we suggest a new theorem in the context of partially ordered metric spaces
Summary
Some remarks on ‘Multidimensional fixed point theorems for isotone mappings in partially ordered metric spaces’. Ravi P Agarwal[1,2], Erdal Karapınar[3,4] and Antonio-Francisco Roldán-López-de-Hierro5*
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