Product Summability Method for Approximation of Lipschitz Functions

This manuscript contributes to summability theory and harmonic analysis by giving a degree of approximation for Fourier series of Lipschitz-class functions via the product mean (C,1) (E,q). We show a theorem regarding estimation of the degree of approximation of functions belonging Lipschitz class by employing the product summability technique applied to the Fourier series corresponding to the function. The new result shows a significant insights into the convergence properties and approximation accuracy of such summation methods within the Lipschitz class. This work underscores the efficacy of product summability techniques in Fourier analysis, revealing their strength in achieving refined approximations and enhancing the theoretical understanding of summability methods in harmonic analysis.