On approximation of signals belonging to some classes by (N,pm,qm)(E,θ)(E,θ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(N,p_m,q_m)(E,\theta )(E,\theta )$$\end{document} means of conjugate series of its Fourier series

In the present study, we approximate the conjugate of the function h denoted by h¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{h}$$\end{document} by a more generalized (N,pm,qm)(E,θ)(E,θ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(N,p_m,q_m)(E,\theta )(E,\theta )$$\end{document} means. Various researchers have studied the degree of approximation in various function spaces such as Lip(α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}), Lip(α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}, r) and Lip(ξ(t),r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi (t),r$$\end{document}), etc. by using product means (C, 2)(E, 1), (E, 1)(C, 1), (E, q) and (N,pn,qn)(E,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(N, p_n, q_n)(E, q)$$\end{document}. Also, they have studied double Euler summability & Nörlund-Euler summability of Fourier and its conjugate series in order to obtain the approximation of functions belonging to different classes. Fourier approximation is a field of great practical significance. Since, the product summability means are stronger than the individual summability means and can be used for approximation for the broader class of functions than by the individual methods. In this way, the system’s stability can be improved by finding the conditions for approximating functions. The established theorem extends, generalizes, and improves various existing results on approximation theory. Also, the result motivates the researcher interested to work with product summability means.