Discussion on Some Recent Order-Theoretic Metrical Coincidence Theorems Involving Nonlinear Contractions

摘要

We prove some coincidence theorems involving a pair of self-mappings f and g defined on an ordered metric space X wherein f is g-increasing phi-contractive mapping. In our results, neither the whole space X nor the range subspaces (f(X) or g(X)) are required to be complete. Instead, we use the completeness of a subspace of X satisfying suitable conditions.