Some new coincidence point results in partial b-metric spaces via digraphs, \mathscr{L}-simulation and \theta-functions

In the present article, we introduce the concept of (\alpha,\theta,\xi)-G-contractive mappings in partial b-metric spaces endowed with a digraph G and discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self mappings satisfying such contractive condition. Our main result will extend several recent results including the well-known Banach contraction theorem. Finally, we exhibit that this extension is viable which will justify the new contractive condition.

کلیدواژه ها:

\mathscr{L}-simulation function ، \theta-function ، weakly compatible maps ، point of coincidence