Abstract
We introduce the concept of the generalized omega(alpha)-contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of omega-distance and alpha-admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature.