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-graphic contraction defined on an extended b-metric space endowed with a graph.