Exploring Fixed Point Results on Double Controlled Metric Spaces

In this study, we explore some fixed point results on double controlled metric spaces by utilizing F and [Formula: see text]-functions. We introduce the notions of generalized [Formula: see text]-contraction and generalized [Formula: see text]-contraction for this purpose. Our findings extend and unify several recent fixed point results. We provide necessary examples to demonstrate the significance of our results. We also apply our results to obtain the existence and uniqueness of a solution to an integral equation.