Some remarks on α-admissibility in S-metric spaces

Abstract

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 α s $\alpha _{s}$ -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 α s $\alpha _{s}$ -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.

Keywords

• α-admissible
• α s $\alpha _{s}$ -admissible
• Generalized rational α s $\alpha _{s}$ -Geraghty contraction type mapping
• S-metric space