Fixed point theorems for generalized $ \alpha $-$ \psi $-contractive mappings in extended $ b $-metric spaces with applications

Abstract

<abstract> In this paper, we introduce a new concept of locally $ \alpha $-$ \psi $-contractive mapping, generalized $ \alpha-\psi $ rational contraction and establish fixed point theorems for such mappings in the setting of extended $ b $-metric space. Our main results extend and improve some results given by some authors. We also provide a non trivial example to show the validity of our main results. As an application, we derive some new fixed point result for $ \psi $-graphic contraction defined on an extended $ b $-metric space endowed with a graph. </abstract>