S-γ-Φ-φ-contractive type mappings in S-metric spaces

In this paper, we introduce several types of S-γ-Φ-φ-contractive mappings which are generalizations of α-ψ contractive mappings [B. Samet, C. Vetro, P. Vetro, Nonlinear Anal., 75 (2012), 2154 ndash;2165] in the structure of Smetric spaces. Furthermore, we prove existence and uniqueness of fixed points and common fixed points of such contractive mappings. Our results generalize, extend and improve the existing results in the literature. We also state some illustrative examples to support our results.