We first present some new existence theorems for fixed point problem and minimization problem in compact metric spaces without assuming that mappings possess convexity property. Some applications of our results to new fixed point theorems for nonself mappings in the setting of strictly convex normed linear spaces and usual metric spaces are also given.
Weng-Seng Heng. Wei-Shih Du. Chi-Lin Yen. "New Existence Results for Fixed Point Problem and Minimization Problem in Compact Metric Spaces." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/635903