The ψ-Framework: An Independently Developed approach

This work presents a ψ-based iterative framework for approximating real solutions of equations.By rewriting equations into fixed-point form and selecting ψ-functions based on root location and interval bounds, solutions can be obtained through repeated iteration. Examples involving quadratic, cubic, quartic, and transcendental equations demonstrate the adaptability of the ψ-framework. The approach highlights how multiple ψ-functions may be constructed for a single equation, with each targeting a specific root.