On the Fixed Points of Large Enriched Contractions in Convex Metric Space with an Application

This paper investigates the fixed points of large enriched contractions in a convex metric space as well as in a convex G-metric space. We establish the sufficient conditions for the existence and uniqueness of fixed points for these mappings. We use the Kransnoselskij-type iterative procedure for the approximation of these fixed points in complete convex metric spaces. We demonstrate that the Kransnoselskij-type iterative approach converges to the unique fixed point associated with large enriched contractions. Our results extend and generalize classical fixed point results by introducing this novel contraction mapping. Some illustrative examples are presented to demonstrate the applicability of our theorems. In the last section, we study the existence of a solution of nonlinear equations as a practical application of our principle findings.