Ekeland variational principle on weighted graphs

In this work, we give a graphical version of the Ekeland variational principle which enables us to discover a new version of the Caristi fixed point theorem in weighted digraphs not necessarily generated by a partial order. Then we show that both graphical versions of the Ekeland variational principle and Caristi's fixed point theorem are equivalent. In addition, we applied our main result on a differential structure Banach space.