Abstract
The concept of α-admissible mapping introduced by Samet et al. (Nonlinear Anal. 75:2154–2165, 2012) has various generalizations. In this paper, we introduce the concept of alpha _{s}-admissible mapping and its various forms by generalizing the concept of α-admissible mapping in the setting of S-metric spaces. Further, we also introduce generalized rational alpha _{s}-Geraghty contraction type mappings and study the existence of fixed point theorems in S-metric spaces. Examples are also given to verify the main results.
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