New Categories of Generalized Fixed Point Theorems in New Generalization of Complete Metric Spaces with an Application

The major objective of this manuscript is to present another novel extension of metric spaces namely; mapping weighted D-complete metric space. In the process, the uniqueness of various strictures of common and common coupled fixed point theorems have been investigated and verified for two pairs of self commutative maps under influence other improved types of extended contractive conditions in these spaces. On the other hand, a novel extended notion of Hausdorff distance namely; Hausdorff ∇∗-distance has been defined in these spaces. Our second main results of various novel types of improved coincidence fixed point theorems have been obtained by applying the conception of generalized Hausdorff ∇∗-distance. Additionally, various practical implementations of the existence fixed point for two pairs of self commutative maps as a solution for certain non-linear Volterra integral equations have been presented and investigated in the framework of map weighted D-complete metric spaces.