On $|A, \delta |_{k}$-summability of orthogonal series
Mathematica Bohemica, Tome 137 (2012) no. 1, pp. 17-25

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
In the paper, we prove two theorems on $|A, \delta |_{k}$ summability, $1\leq k\leq 2$, of orthogonal series. Several known and new results are also deduced as corollaries of the main results.
In the paper, we prove two theorems on $|A, \delta |_{k}$ summability, $1\leq k\leq 2$, of orthogonal series. Several known and new results are also deduced as corollaries of the main results.
DOI : 10.21136/MB.2012.142785
Classification : 40A05, 40C05, 40D15, 40F05, 42C05, 42C15
Keywords: orthogonal series; matrix summability
Krasniqi, Xhevat Z. On $|A, \delta |_{k}$-summability of orthogonal series. Mathematica Bohemica, Tome 137 (2012) no. 1, pp. 17-25. doi: 10.21136/MB.2012.142785
@article{10_21136_MB_2012_142785,
     author = {Krasniqi, Xhevat Z.},
     title = {On $|A, \delta |_{k}$-summability of orthogonal series},
     journal = {Mathematica Bohemica},
     pages = {17--25},
     year = {2012},
     volume = {137},
     number = {1},
     doi = {10.21136/MB.2012.142785},
     mrnumber = {2978443},
     zbl = {1249.42018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2012.142785/}
}
TY  - JOUR
AU  - Krasniqi, Xhevat Z.
TI  - On $|A, \delta |_{k}$-summability of orthogonal series
JO  - Mathematica Bohemica
PY  - 2012
SP  - 17
EP  - 25
VL  - 137
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2012.142785/
DO  - 10.21136/MB.2012.142785
LA  - en
ID  - 10_21136_MB_2012_142785
ER  - 
%0 Journal Article
%A Krasniqi, Xhevat Z.
%T On $|A, \delta |_{k}$-summability of orthogonal series
%J Mathematica Bohemica
%D 2012
%P 17-25
%V 137
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2012.142785/
%R 10.21136/MB.2012.142785
%G en
%F 10_21136_MB_2012_142785

[1] Okuyama, Y.: On the absolute Nörlund summability of orthogonal series. Proc. Japan Acad. 54 (1978), 113-118. | MR | Zbl

[2] Okuyama, Y., Tsuchikura, T.: On the absolute Riesz summability of orthogonal series. Anal. Math. 7 (1981), 199-208. | DOI | MR | Zbl

[3] Tanaka, M.: On generalized Nörlund methods of summability. Bull. Austral. Math. Soc. 19 (1978), 381-402. | DOI | MR | Zbl

[4] Okuyama, Y.: On the absolute generalized Nörlund summability of orthogonal series. Tamkang J. Math. 33 (2002), 161-165. | MR

[5] Flett, T. M.: On an extension of absolute summability and some theorems of Littlewood and Paley. Proc. London Math. Soc. 7 (1957), 113-141. | MR | Zbl

[6] Flett, T. M.: Some more theorems concerning the absolute summability of Fourier series and power series. Proc. London Math. Soc. 8 (1958), 357-387. | MR | Zbl

[7] Lal, S.: Approximation of functions belonging to the generalized Lipschitz Class by $C^{1}\cdot N_{p}$ summability method of Fourier series. Appl. Math. Comput. 209 (2009), 346-350. | DOI | MR | Zbl

Cité par Sources :