On enriched condensed Kannan-type contractions in normed spaces with applications to variational inequality problems

Abstract

In this paper, we introduce a new class of condensed Kannan-type contractions in normed spaces and establish several fixed point results for nonlinear operators satisfying the proposed contractive condition. By employing the Krasnoselskii iterative scheme, we establish an existence theorem for the proposed class of mappings that guarantees the approximation of solutions to both unique and non-unique fixed point problems. We further investigate the Ulam-Hyers stability of the associated fixed point problem. Several numerical examples are presented to illustrate the applicability and effectiveness of the theoretical findings. As an application, the results are utilized to study variational inequality problems. This demonstrates the usefulness of the proposed framework in nonlinear analysis and related optimization problems.