Generalized matrix summability of a conjugate derived Fourier series

Abstract

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
• conjugate Fourier series
• conjugate derived Fourier series
• ( E , q ) $(E,q)$ -summability
• ( E , q ) ( N ¯ , p n ) $(E,q)(\bar{N},p_{n})$ -summability
• F B $F_{\mathfrak{B}}$ -convergence