A New Approach of Proinov-Type Contractions on Metric Spaces

In this paper, we define the classes of Proinov $D-$contraction and generalized Proinov $D-$contraction which are properly larger than the classes of $(\psi,\varphi)-$contraction and generalized $(\psi,\varphi)-$contraction studied by Proinov (2020) and improved and corrected by Popescu (2021). Also, the given results are a real generalization of Banach's contraction principle, \'Ciri\'c (1971) and Boyd and Wong (1969). The given examples demonstrate that our results generalize the results announced by Popescu and Proinov effectively and robustly.