Abstract

The aim of this paper is to introduce an inertial Picard–CR iterative method for approximating fixed points of a family of nonexpansive mappings in real Hilbert spaces. The proposed method is designed to improve the convergence performance of existing schemes while maintaining simplicity in implementation. Under suitable conditions, we establish strong convergence results for the proposed iterative process. We apply the algorithm to solve split feasibility problems, signal processing problems, polynomiography problems, fractional differential, and integral equations. Several numerical experiments demonstrating the superiority of the proposed method over existing methods are presented. The obtained results extend and improve several known results in the literature.

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