some new coincidence point results in partial b-metric spaces via digraphs, l -simulation and θ-functions

In the present article, we introduce the concept of (α, θ, ξ)-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.