Approximation Properties of Product Means of Fourier Series
Priyadarshani Behera
Department of Mathematics, DRIEMS University, Tangi, Cuttack-754022, India.
Ranjan Kumar Jati *
Department of Mathematics, DRIEMS University, Tangi, Cuttack-754022, India.
Nirmal Chandra Sahu
Department of Mathematics, DRIEMS University, Tangi, Cuttack-754022, India.
*Author to whom correspondence should be addressed.
Abstract
The degree of approximation is an important concept in many areas of mathematics, especially in mathematical modeling and scientific computing, where accurate approximations are necessary for dependable predictions and simulations. In this work, we establish a new theorem for estimating the degree of approximation of functions belonging to the Lipschitz class by applying a product summability technique to their associated Fourier series. The results provide improved convergence behavior and sharper error estimates compared with classical single summability techniques. Such studies are valuable for advancing theoretical developments in harmonic analysis and summability theory, which have various applications in signal processing, numerical analysis, and mathematical modeling.
Keywords: Degree of approximation, Lipschitz class functions, Lip (ξ(t),r)), Cesaro mean, Euler mean, product summability, Fourier series, Big O