On the absolute Nörlund summability of orthogonal series

On Absolute Almost Generalized Nörlund Summability of Orthogonal Series

“…It involves a sequence that satisfies certain conditions. During the proof of this theorem is used a similar method with one of Okuyama [18], and Ul'yanov [29].…”

“…The absolute Nörlund summability, the absolute generalized Nörlund summability, the absolute Riesz summability, absolute generalized Cesàro summability, absolute Euler summability of an orthogonal series has been studied by many authors. For example, one can see the work of Tandori [27], Leindler [12]- [15], Okuyama and Tsuchikura [20], Okuyama [18]- [22], Szalay [26], Billard [2], Grepaqevskaya [4], Spevakov and Kudrajatsev [25]. In 2002 Okuyama [23] using generalized Nörlund means has proved two theorems which give sufficient conditions in terms of the coefficients of an orthogonal series under which it is absolute generalized Nörlund summable almost everywhere.…”

Certain sufficient conditions on |N,pn,qn|k summability of orthogonal series

“…). Our main purpose of the present paper is to study the |N, p n , q n | k summability of the orthogonal series (1.1), for 1 ≤ k ≤ 2, and to deduce as corollaries all results of Y. Okuyama [6].…”

On absolute generalized Hausdorff summability of orthogonal series

“…On the other hand, by many authors such notions are employed to study an interesting topic in theory of orthogonal series the so-called their absolute summability. For example, one can see the work of Tandori [19], Leindler [8][9][10][11], Okuyama and Tsuchikura [15], Okuyama [13,14], Szalay [17], Billard [1], Grepaqevskaya [4], Spevakov and Kudrajatsev [16]. In 2002 Okuyama [14] using generalized Nörlund means has proved two theorems which give sufficient conditions in terms of the coefficients of an orthogonal series under which it is absolute generalized Nörlund summable almost everywhere.…”