A theorem on local property of |N̄,pn|k summability of factored Fourier series, which generalizes some known results, and also a general theorem concerning the |N̄,pn|k summability factors of Fourier series have been proved.

Abstract This paper explores the possibility for summing Fourier series nonlinearly via Pythagorean harmonic mean. It reports on new results this summability with introduction of concepts like smoothing operator and semi-harmonic summation. The is demonstrated to be Kalman filtering linear summability, logistic processing linearized summability. An emerging direct inapplicability seismic-like s...

We investigate non-adaptive methods of deep ReLU neural network approximation in Bochner spaces L2(U∞,X,μ) functions on U∞ taking values a separable Hilbert space X, where is either R∞ equipped with the standard Gaussian probability measure, or [−1,1]∞ Jacobi measure. Functions to be approximated are assumed satisfy certain weighted ℓ2-summability generalized chaos polynomial expansion coeffici...

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

In [1] Agnew presented the following theorem: if x is a bounded sequence and A is a regular summability matrix, then there exists a subsequence y of x such that each limit point of x is a limit point of Ay. Fridy [2] extended this result by replacing subsequence with rearrangement. Keagy [3] presented two theorems that strengthened the results of both Agnew and Fridy. This was accomplished by w...

In this paper we prove some Tauberian theorems for the product of Borel and Hölder summability methods which improve the classical Tauberian theorems for the Borel summability method. Mathematics Subject Classification 2010: 40E05, 40G05, 40G10.

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...

In this paper, a known theorem dealing with | C, 1 |k summability methods has been generalized under weaker conditions for | C, α, β ; δ |k summability methods. Some new results have also been obtained. AMS subject classifications: 40D15, 40F05, 40G99