Comparable nonlinear contractions in ordered metric spaces

In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, g continuity and compatibility to ordertheoretic setting especially in ordered metric spaces and utilize these relatively weaker notions to prove some existence and uniqueness results on coincidence points for g-comparable mappings satisfying BoydWong type nonlinear contractivity conditions. We also furnish some illustrative examples to demonstrate our results. Finally, as an application of our certain newly proved results, we establish the existence and uniqueness of solution of an integral equation.