Approximation on Fixed Point for F-Iterative Scheme

Abstract

In this paper, we study the approximation of fixed points of mappings satisfying the (η,θ)-condition in uniformly convex Banach spaces. Using the F-iterative scheme, we establish weak and strong convergence results under suitable assumptions. Our results extend and generalize several existing fixed point theorems, including those for Suzuki-type mappings. Finally, the applicability of the proposed (η,θ)-condition and the associated iterative scheme is demonstrated through an image restoration problem, supported by numerical experiments.