However, [ 8 ] observed that the fixed point obtained in the above Theorem 1.2 is not necessarily unique. Hence, a robust version of the results in [ 7 ] is provided therein. For some extensions of the idea of interpolative contractions in fixed point theory, we refer to [ 9 , 10 ] and the references therein. Following Petruşel and Rus [ 11 ], a self-mapping T of a metric space ( X, d ) is said to be a Picard operator (abbr., PO ) if T has a unique fixed point x ∗ and lim n →∞ T n x = x ∗ for all x ∈ X and T is said to be a weakly Picard operator (abbr. WPO ) if the sequence { T n x } n ∈ N converges, for all x ∈ X and the limit (which may depend on x ) is a fixed point of T . Jachymski [ 12 ] introduced the notion of contraction in metric space endowed with a graph G . Accordingly, let ( X, d ) be a metric space and let ∆ denote the diagonal of the Cartesian product X × X . Consider a directed graph G such that the set V ( G ) of its vertices coincides with X , and the set E ( G ) of its edges contains all loops, i.e., E ( G ) ⊇ ∆ . It is assumed that G has no parallel edges, so G can be identified with the pair ( V ( G ) , E ( G )) . Moreover, G may be treated as a weighted graph (see [ [ 13 ], p. 376]) by assigning to each edge the distance between its vertices. Denote by G − 1 , the conversion of a graph G , i.e., the graph obtained from G by reversing the direction of edges. Therefore,