In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

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.

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.

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

*Correspondence: [email protected] 1Faculty of Education, Harran University, Şanlıurfa, Turkey Full list of author information is available at the end of the article Abstract New concepts of fλ,μ-statistical convergence for double sequences of order α̃ and strong fλ,μ-Cesàro summability for double sequences of order α̃ are introduced for sequences of (complex or real) numbers. Furthermore, we giv...

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...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of a μ-almost equicontinuous cellular automata F , converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. ...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of such automata converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. Therefore we also show that for an...

The forward estimation problem for stationary and ergodic time series {X n } ∞ n=0 taking values from a finite alphabet X is to estimate the probability that X n+1 = x based on the observations X i , 0 ≤ i ≤ n without prior knowledge of the distribution of the process {X n }. We present a simple procedure g n which is evaluated on the data)| → 0 almost surely for a subclass of all stationary an...

In the present study, we construct a new matrix which call quasi-Cesaro and is generalization of ordinary Cesaro matrix, introduce $BK$-spaces $C^q_k$ $C^q_{\infty}$ as domain $C^q$ in spaces $\ell_k$ $\ell_{\infty},$ respectively. Furthermore, exhibit some topological properties inclusion relations related to these newly defined spaces. We determine basis space obtain Köthe duals $C^q_{\infty}...