# Best approximation of conjugate of a function in generalized Zygmund

## DOI:

https://doi.org/10.5556/j.tkjm.50.2019.3006## Keywords:

Generalized Zygmund class, error approximation, conjugate Fourier series, Matix- Euler (TEq) product means, generalized Minkowski’s inequality## Abstract

In this paper, we, for the very first time, study the error estimates of conjugate of a function ~g of g

(2-periodic) in generalized Zygmund class Y w

z (z 1); by Matix-Euler (TEq) product operator

of conjugate Fourier series. In fact, we establish two theorems on degree of approximation of a

function ~g of g (2-periodic) in generalized Zygmund class Y w

z (z 1); by Matix-Euler (TEq)

product means of its conjugate Fourier series. Our main theorem generalizes three previously

known results. Thus the results of [7], [8] and [26] become the particular cases of our Theorem

2.1. Some corollaries are also deduced from our main theorem.

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## How to Cite

*Tamkang Journal of Mathematics*,

*50*(4), 417-427. https://doi.org/10.5556/j.tkjm.50.2019.3006