Mathematics and Computer Science, Volume 1

1Error Estimation of the Function by Using Product Means of the Conjugate Fourier Series

Aradhana Dutt Jauhari* and Pankaj Tiwari

Division of Mathematics, Department of Basic Sciences, Galgotias University, Greater Noida, G. B. Nagar, U.P., India

Abstract

The purpose of the current chapter is to attain the best result on a new way and the best approximation of different classes of the work, which has been discussed by different mathematician under different summability means. Here, we are presenting the theorems established under means of the CFS of a signal, belongs to Some known and unknown results have been proven by many mathematicians. But this is a new and unique way of proving a new result.

Keywords: Generalized Zygmund class product means, Degree of Approximation (DoA), Conjugate Fourier Series (CFS)

1.1 Introduction

Let, us take ∑a_n − an infinite series and s_n − the sequence of partial sums. Also, {p_n} and {q_n} are the sequences of positive real numbers s.t.-

1.1.1 ...