Existence Theorems for Generalized Distance on Complete Metric Spaces

We first introduce the new concept of a distance called u-distance, which generalizes omega-distance, Tataru's distance, and tau-distance. Then we prove a new minimization theorem and a new fixed point theorem by using a u-distance on a complete metric space. Our results extend and unify many known results due to Caristi, Ciric, Ekeland, Kada-Suzuki-Takahashi, Kannan, Ume, and others.