Some coincidence theorems for generalized nonlinear contractions in ordered metric spaces with applications

Abstract

Abstract In this article, we prove some existence and uniqueness results on coincidence points for g-increasing mappings satisfying generalized φ-contractivity conditions in ordered metric spaces. As an application of one of our newly proved results, we indicate the formulation of a coupled coincidence theorem. Our results generalize, extend, modify, improve, sharpen, enrich, and complement several well-known results of the existing literature. Also, we point out that a recent coincidence point result proved in Dalal et al. (J. Adv. Math. 7(1):1084-1094, 2014) contains errors and omissions. MSC:47H10, 54H25.