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Inspired by the recent result of N. Hussain et al. [N. Hussain, E. Karapinar, P. Salimi, F. Akbar, α-admissible mappings and related fixed point theorems, Journal of Ineaqualities and Applications 2013, 2013:114] we introduced two new type functions, which we denoted as upclass of type II and αβ -contractive mappings. Specifically, all results of the mentioned paper is possible to generalize using this two types of functions.

Αβ - contractive mappings and upclass of type II function