In this paper, we continue our investigations in line of our recent papers, Savas and Das [16] and Das, Savas and Ghosal [5]. We introduce the notion of AI statistical convergence which includes the new summability methods studied in [16] and [5] as special cases and make certain observations on this new and more general summability method.

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.

The concept of statistical convergence of a sequence was first introduced by H. Fast. Statistical convergence was generalized by R. C. Buck, and studied by other authors, using a regular nonnegative summability matrix A in place of C\ . The main result in this paper is a theorem that gives meaning to the statement: S= {sn} converges to L statistically (T) if and only if "most" of the subsequenc...

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.

*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...

Recently, for single series, the necessary and sufficient conditions $\left\vert C,0\right\vert\Rightarrow \left\vert A_{f}\right\vert_{k}$ vise versa, A_{f}\right\vert \Rightarrow C,0\right\vert_{k}$ versa have been established, where $1 < k \infty $ $A$ is a factorable matrix. The present study extends these results to double summability, also provides some new results.