We introduce the notion of weaker -contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.
Chi-Ming Chen. W. Y. Sun. "Periodic Points and Fixed Points for the Weaker -Contractive Mappings in Complete Generalized Metric Spaces." J. Appl. Math. 2012 1 - 7, 2012. https://doi.org/10.1155/2012/856974