The aim of this paper is to obtain some (common) fuzzy fixed point theorems for fuzzy mappings concerning F- contractions (the concept was introduced in [Wardowski, Fixed Point Theory and Applications, 94 (2012), 1-6]) and Feng - Liu type condition [Feng and Liu, Journal of Mathematical Analysis and Applications, 317 (2006) 103-112] in compelete metric spaces with/without using the Pompeiu - Hausdorff distance between α-level sets of fuzzy mappings. Our results generalize and strengthen various known results in the literature. An example and an application for the solution of a system of functional equations arising in dynamic programming are given to illustrate the usability of the obtained results.
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