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In this article, we generalize some frequently used metrical notions such as: completeness, continuity, g-continuity, and compatibility to order-theoretic setting especially in ordered metric spaces besides introducing some new notions such as: the ICC property, DCC property, MCC property etc. and utilize these relatively weaker notions to prove some coincidence theorems for g-increasing Boyd-Wong type contractions which enrich some recent results due to Alam et al. (Fixed Point Theory Appl. 2014:216, 2014).

Enriching some recent coincidence theorems for nonlinear contractions in ordered metric spaces