On Picard-CR iterations involving weak perturbative contraction operators and application to reversible chemical reactions

Abstract

We propose an efficient iterative method called Picard-CR for approximating fixed points under weak perturbative contraction conditions in uniformly convex hyperbolic metric spaces. Theoretical analysis establishes both weak and strong convergence, with performance validated against classical methods (CR, Picard-Noor, and Picard-SP) through numerical experiments. We extend our convergence results to non-expansive and contraction mappings, supported by MATLAB-based visualizations. The iterative scheme is shown to be stable and more efficient, with direct application to computing equilibrium concentrations in reversible chemical reactions. Our findings contribute not only to fixed point theory but also provide practical computational tools for chemical and engineering problems.