An Essential Remark on Relation-Theoretic Metrical Fixed Point Results - Senapati, Tanusri; Dey, Lakshmi Kanta (Communications in Mathematics and Applications, 2018)
In this short note, we notice that the relation-theoretic metrical fixed point results are equivalent with the fixed point results in \(α\)-complete metric spaces. We observe that any arbitrary binary relation on a non empty set \(X\) can be defined in terms of an arbitrary real valued function defined on \(X× X\). Consequently we show that the results of Alam and Imdad (J. Fixed Point Theory Appl. 17(4) (2015)) and Ahmadullah et al. (arXiv) do not contribute anything new in the literature.