Common fixed points for generalized $$\alpha $$ α -implicit contractions in partial metric spaces: consequences and application

Abstract

In this paper, we introduce the concept of generalized \(\alpha \)-admissible pair of mappings generalizing the definition of \(\alpha \)-admissible mappings presented by Samet et al. (Nonlinear Anal 75:2154–2165, 2012). Based on above, we define generalized \(\alpha \)-implicit contractions in the setting of partial metric spaces and we provide some common fixed point results for such contractions. We also derive some consequences and corollaries from our obtained results. An application and some examples are presented making effective the new concepts and results.