Trigonometric Approximation of Signals Belonging to  \(Lip(\xi (t), r)\) Class by  \((C, 1)(N,p_m,q_m)(E,\theta )\) Means of Conjugate Fourier Series

Various authors have studied the trigonometric or Fourier approximation in various function spaces using different means (C, 2)(E, 1), (E, q) and \((N, p_n, q_n)(E, q)\) , etc. In our study, we approximate the functions belonging to different classes by a more generalized \((C, 1)(N,p_m,q_m)(E,\theta )\) means of conjugate Fourier series. The discipline of Fourier approximation holds significant practical importance. Because the product summability means can be used to approximate functions and are stronger than the individual summability means. Additionally, approximation theory is used to identify the degree of approximation and to solve engineering problems by approximating the function and minimizing error. The established theorem builds, expands, and generalizes a number of previous approximation theory conclusions. Additionally, the outcome encourages researchers who are interested in working with product summability measures.