Generalized matrix summability of a conjugate derived Fourier series

M Mursaleen; Abdullah Alotaibi

doi:10.1186/s13660-017-1542-5

Generalized matrix summability of a conjugate derived Fourier series

J Inequal Appl. 2017;2017(1):273. doi: 10.1186/s13660-017-1542-5. Epub 2017 Nov 2.

Authors

M Mursaleen^{1

2}, Abdullah Alotaibi²

Affiliations

¹ Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
² Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589 Saudi Arabia.

Abstract

The study of infinite matrices is important in the theory of summability and in approximation. In particular, Toeplitz matrices or regular matrices and almost regular matrices have been very useful in this context. In this paper, we propose to use a more general matrix method to obtain necessary and sufficient conditions to sum the conjugate derived Fourier series.

Keywords: Fourier series; [Formula: see text]-convergence; [Formula: see text]-summability; conjugate Fourier series; conjugate derived Fourier series.