On Absolute Almost Generalized Nörlund Summability of Orthogonal Series

• Journal title : Kyungpook mathematical journal
• Volume 52, Issue 3,  2012, pp.279-290
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2012.52.3.279
Title & Authors
On Absolute Almost Generalized Nörlund Summability of Orthogonal Series
Krasniqi, Xhevat Zahir;

Abstract
In this paper we present some results on absolute almost generalized N$\small{\ddot{o}}$rlund summability of orthogonal series. The most important corollaries of the main results also are deduced.
Keywords
Orthogonal series;N$\small{\ddot{o}}$rlund summability;
Language
English
Cited by
References
1.
G. Alexits, Convergence problems of orthogonal series, Translated from the German by I. Folder. International Series of Monographs in Pure and Applied Mathematics, Vol. 20, Pergamon Press, New York-Oxford-Paris 1961, 350 pp.

2.
P. Billard, Sur la sommabilite absolue des series de functions orthogonales, (French) Bull. Sci. Math., 85(1961), 29-33.

3.
T. M. Flett, On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. London Math. Soc., 7(1957), 113-141.

4.
L. V. Grepachevskaya, Absolute summability of orthogonal series, (Russian) Mat. Sb. (N. S.), 65(107)(1964), 370-389.

5.
G. H. Hardy, Divergent Series, first edition, Oxford University Press, 1949.

6.
Xh. Z. Krasniqi, A note on |N,p,q|k $(1\;{\leq}\;K\;{\leq}\;2)$ summability of orthogonal series, Note Mat., 30(2)(2010), 135-139.

7.
Xh. Z. Krasniqi, On absolute generalized Norlund summability of double orthogonal series, Int. J. Nonlinear Anal. Appl., 2(2)(2011), 63-75.

8.
Xh. Z. Krasniqi, On absolutely almost convergency of higher order of orthogonal series, Int. J. Open Problems Comput. Sci. Math., 4(1)(2011), 44-51.

9.
Xh. Z. Krasniqi, Certain sufficient conditions on $|N,p_{n},q_{n}|k$ summability of orthogonal series, J. Nonlinear Sci. Appl., (to appear).

10.
Xh. Z. Krasniqi, On absolute weighted mean summability of orthogonal series, Selcuk J. Appl. Math. Appl., 12(2)(2011), 63-70.

11.
Xh. Z. Krasniqi, On $|A,{\delta}|_k$-summability of orthogonal series, Math. Bohem., 137(1)(2012), 17-25.

12.
L. Leindler, Uber die absolute summierbarkeit der orthogonalreihen, (German) Acta Sci. Math. (Szeged), 22(1961), 243-268.

13.
L. Leindler, On the absolute Riesz summability of orthogonal series, Acta Sci. Math. (Szeged), 46(1-4)(1983), 203-209.

14.
L. Leindler and K. Tandori, On absolute summability of orthogonal series, Acta Sci. Math. (Szeged), 50(1-2)(1986), 99-104.

15.
L. Leindler, On the newly generalized absolute Riesz summability of orthogonal series, Anal. Math., 21(4)(1995), 285-297.

16.
G. G. Lorentz, A contribution to the theory of divergent series, Acta Math., 80(1948), 167-190.

17.
S. M. Mazhar, A. H. Siddiqi, On olmost summability of a trigonometric sequence, Acta Math. Acad. Sci. Hungar., 20(1969), 21-24.

18.
Y. Okuyama, On the absolute Norlund summability of orthogonal series, Proc. Japan Acad., 54(1978), 113-118.

19.
Y. Okuyama, On the absolute Norlund summability of orthogonal series, Proc. Japan Acad. Ser. A Math. Sci., 54(5)(1978), 113-118.

20.
Y. Okuyama and T. Tsuchikura, On the absolute Riesz summability of orthogonal series, Analysis Math., 7(1981), 199-208.

21.
Y. Okuyama, Absolute summability of Fourier series and orthogonal series. Lecture Notes in Mathematics, 1067. Springer-Verlag, Berlin, 1984, 118 pp.

22.
Y. Okuyama, On the absolute Riesz summability of orthogonal series, Tamkang J. Math. 19(3)(1988), 75-89.

23.
Y. Okuyama, On the absolute generalized Norlund summability of orthogonal series, Tamkang J. Math., 33(2002), 161-165.

24.
K. Qureshi, On the degree of approximation of a periodic function f by almost Norlund means, Tamkang J. Math., 12(1)(1981), 35-38.

25.
V. N. Spevakov, B. A. Kudrjavcev, Absolute summability of orthogonal series by the Euler method, (Russian) Mat. Zametki, 21(1)(1977), 51-56.

26.
I. Szalay, On generalized absolute Cesaro summability of orthogonal series, Acta Sci. Math. (Szeged), 32(1971), 51-57.

27.
K. Tandori, Uber die orthogonalen Funktionen IX (Absolute Summation), Acta Sci. Math. (Szeged), 21(1960), 292-299.

28.
M. Tanaka, On generalized Norlund methods of summability, Bull. Austral. Math. Soc., 19(1978), 381-402.

29.
P. L. Ulyanov, Solved and unsolved problem in the theory of trigonometric and orthogonal series, Uspehi Math. Nauk., 19(1964), 3-69 .