Best approximation of conjugate of a function in generalized Zygmund

  • Hare Krishna Nigam Associate Professor and Head, Department of Mathematics, Central University of South Bihar, Gaya, Bihar, India
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.

Author Biography

Hare Krishna Nigam, Associate Professor and Head, Department of Mathematics, Central University of South Bihar, Gaya, Bihar, India
Associate Professor and Head, Department of Mathematics

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Published
2019-12-30
How to Cite
Nigam, H. K. (2019). Best approximation of conjugate of a function in generalized Zygmund. Tamkang Journal of Mathematics, 50(4), 417-427. https://doi.org/10.5556/j.tkjm.50.2019.3006
Section
Papers