A gap in the paper "A note on cone metric fixed point theory and its equivalence" [Nonlinear Anal. 72(5), (2010), 2259-2261]

TL;DR

This paper identifies and corrects a gap in a previously published theorem on cone metric fixed point theory, ensuring the accuracy and completeness of the mathematical results.

Contribution

It highlights a specific flaw in Du's 2010 theorem and provides a corrected version to strengthen the theoretical foundation.

Findings

The original theorem contained a gap that affected its validity.

The authors successfully repair the theorem, restoring its correctness.

The correction clarifies the conditions under which the fixed point results hold.

Abstract

There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.