Abstract
In this paper, we prove sharpened versions of some classical order-theoretic metrical fixed point theorems due to Nieto and Rodriguez-Lopez (Order 22(3): 223-239, 2005) using order-theoretic variants of completeness and continuity besides some another notions such as: the ICC property, the DCC property, and the MCC property. In this continuation, we further extend our results for Boyd-Wong type nonlinear contractions. Finally, as an application of our certain newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.