Fixed- and Attractive-Point Results for Enriched Cλg-Nonexpansive Mappings with Application

In this paper, we introduce a new class of mappings called enriched Cλg-nonexpansive mappings, which extends the class of g-nonexpansive mappings employing an enriched Cλ-type condition. We discuss the existence of its fixed point and approximation of generalized g-attractive points associated with the proposed class of mappings. In particular, we study several structural properties of the corresponding attractive point set and develop a g-averaged viscosity-type iterative scheme to approximate its elements. Under suitable assumptions for the control sequences, we prove the strong convergence of the generated sequence to a generalized g-attractive point. Fixed-point and coincidence-point results are thus obtained as special cases of the proposed approach. As an application, we apply our result to find the existence of the best approximations. We also illustrate the applicability of the proposed iteration method through a numerical experiment. The numerical results demonstrate the effect of the parameter λ on the convergence behavior and show that larger values of λ provide better numerical performance for the considered example.