Absolute and strong summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series and $r$ times differentiated conjugate Fourier series by matrix methods

We establish conditions of $|\gamma|_p$- and $[\gamma]_p$-summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series at the point where $\gamma = \| \gamma_{nk} \|$ is the matrix of transformation of series to sequence. Analogous conditions are considered also for $r$ times differentiated conjugate Fourier series.

Tauberian theorems in the case of strong summability in degree $p$ of double series

We establish a Tauberian theorem in the case of strong summability in degree $p$ of double series by matrix methods, give its application to Abel methods.

Absolute and strong summability in degree $p \geqslant 1$ of series, associated with Fourier series, by matrix methods

We establish conditions of $|\gamma|_p$- and $[\gamma]_p$-summability in degree $p \geqslant 1$ of series, associated with Fourier series, at the point where $\gamma = \| \gamma_{nk} \|$ is the matrix of transformation of series to sequence.

Pointwise (H, Φ) Strong Approximation by Fourier Series of LΨ Integrable Functions

We essentially extend and improve the classical result of G. H. Hardy and J. E. Littlewood on strong summability of Fourier series. We will present an estimation of the generalized strong mean (H, Φ) as an approximation version of the Totik type generaliza- tion of the result of G. H. Hardy, J. E. Littlewood, in case of integrable functions from LΨ. As a measure of such approximation we will use the function constructed by function Ψ com- plementary to Φ on the base of definition of the LΨ points. Some corollary and remarks will also be given.

Strong Riesz summability of Fourier series

The notion of strong summability was introduced by Fekete (Math. És Termesz Ertesitö, 34 (1916), 759-786). Dealing with Nörlund summability of Fourier series Mittal (J. Math. Anal. Appl. 314 (2006), 75-84) has established a result on strong summability. We have established a new result on sufficient condition for strong Riesz summability of Fourier series.

A note on the strong summability of two-dimensional Walsh–Fourier series

In this paper, we investigate the strong summability of two-dimensional Walsh–Fourier series obtained in [F. Weisz, Strong convergence theorems for two-parameter Walsh–Fourier and trigonometric-Fourier series, Studia Math. 117 1996, 2, 173–194] (see Theorem W) and prove the sharpness of this result.

λ-double statistical convergence of functions

In this paper, the definitions of ?-double strong summability and ?-double statistical convergence for real valued measurable functions of two variables defined on (1,?)x(1,?) are presented. Using these definitions we present a series of basic results. Additionally, inclusion theorems, extension of existing results in the literature, and their variations have been established.