In this paper, we introduce the notions of Z Γ −contractions and Suzuki Z Γ-contractions via Γ−simulation functions. By using these new contractions, we extend and unify several existing fixed point results in the corresponding literature. We also show that the recently defined notion of L −simulation function is an special case of Z Γ −contraction. In addition, some notable examples are given to illustrate and support the obtained results.