The existence theorem for a coincidence point of some admissible contraction mappings in a generalized metric space

Abstract

© 2020 by the Mathematical Association of Thailand. In the current study, we focus on finding a coincidence point of two certain mappings that are defined on a generalized metric space. These mappings are assumed to have some admissible contraction property of a specific kind based on the generalized metric. Our main results provide the sufficient conditions to the existence of a coincidence point of the mappings. Further, we give an example satisfying all conditions to support our main theorem. Finally, the result is applied to the integral equation. Specifically, we obtain some assumptions to guarantee the existence of a solution when the equation is homogeneous.