Araştırma Makalesi
BibTex RIS Kaynak Göster

Summability factors between the absolute Cesàro methods

Yıl 2018, , 1923 - 1926, 01.12.2018
https://doi.org/10.16984/saufenbilder.470493

Öz

If Σε_{n}x_{n} is summable by the method Y whenever Σx_{n} is summable by the method X, then we say that the factor ε=(ε_{n}) is of type (X,Y) and denote by (X,Y). In this study we characterize the sets (|C,α|_{k},|C,-1|) , k>1 and (|C,-1|,|C,α|_{k}) , k≥1 for α>-1. Also, in the special case, we give some inclusion relations between methods, which completes some open problems in literature.

Kaynakça

  • [1] Bor, H., Some equivalence theorems on absolute summability methods, Acta Math. Hung.,149, (2016) 208-214.[2] Bor, H. and Thorpe, B., On some absolute summability methods, Analysis 7 (2) (1987),145-152.[3] Bor, H., On two summability methods, Math. Proc. Cambridge Philos Soc. 98, (1985),147-149.[4] Flett, T.M., On an extension of absolute summability and some theorems of Littlewoodand Paley, Proc. London Math. Soc. 7 (1957), 113-141.[5] Hardy, G. H., Divergent Series, Oxford, 1949.[6] Hazar, G. C. and Sar¬göl M. A., Compact and Matrix Operators on the Space jC;􀀀1jk,J. Comput. Anal. Appl., 25(6), (2018), 1014-1024.[7] Hazar, G. C. and Sar¬göl M. A., On factor relations between weighted and Nörlund means,Tamkang J. Math. (in press)[8] Kogbetliantz, E., Sur lesseries absolument sommables par la methods des moyannes arith-metiques, Bull. des Sci. Math. 49 (1925), 234-256.[9] Maddox, I.J., Elements of functinal analysis, Cambridge University Press, London, NewYork, (1970).[10] Mazhar, S.M., On the absolute summability factors of in…nite series, Tohoku Math. J.,23(1971), 433-451.[11] Mehdi, M.R., Summability factors for generalized absolute summability I, Proc. LondonMath. Soc.(3), 10 (1960), 180-199.[12] Mohapatra, R. N., On absolute Riesz summability factors, J. Indian Math. Soc. 32(1968),113-129.[13] Orhan, C. and Sar¬göl, On absolute weighted mean summability, Rocky Mount. J. Math.23 (1993), 1091-1097.[14] Sarıgöl, M.A., Spaces of series Summable by absolute Cesàro and Matrix Operators ,Comm. Math. Appl. 7(1), (2016), 11-22.[15] Sarıgöl, M.A., Extension of Mazhar’s theorem on summability factors, Kuwait J. Sci. 42(3) (2015), 28-35.[16] Sarıgöl, M.A., On the local properties of factored Fourier series, Appl. Math. Comp., 216(2010), 3386-3390.[17] Sarıgöl, M.A., and Bor, H., Characterization of absolute summability factors, J. Math.Anal. Appl. 195 (1995), 537-545.[18] Sarıgöl, M.A., On two absolute Riesz summability factors of in…nite series, Proc. Amer.Math. Soc. 118 (1993), 485-488.[19] Sarıgöl, M.A., A note on summability, Studia Sci. Math. Hungar. 28 (1993), 395-400.[20] Sulaiman, W.T., On summability factors of in…nite series, Proc. Amer. Math. Soc. 115(1992), 313-317.[21] Sulaiman, W.T., On some absolute summability factors of In…nite Series, Gen. Math.Notes, 2 (2) (2011), 7-13.[22] Thorpe, B., Matrix transformations of Cesàro summable Series, Acta Math. Hung., 48(3-4), (1986), 255-265.
Yıl 2018, , 1923 - 1926, 01.12.2018
https://doi.org/10.16984/saufenbilder.470493

Öz

Kaynakça

  • [1] Bor, H., Some equivalence theorems on absolute summability methods, Acta Math. Hung.,149, (2016) 208-214.[2] Bor, H. and Thorpe, B., On some absolute summability methods, Analysis 7 (2) (1987),145-152.[3] Bor, H., On two summability methods, Math. Proc. Cambridge Philos Soc. 98, (1985),147-149.[4] Flett, T.M., On an extension of absolute summability and some theorems of Littlewoodand Paley, Proc. London Math. Soc. 7 (1957), 113-141.[5] Hardy, G. H., Divergent Series, Oxford, 1949.[6] Hazar, G. C. and Sar¬göl M. A., Compact and Matrix Operators on the Space jC;􀀀1jk,J. Comput. Anal. Appl., 25(6), (2018), 1014-1024.[7] Hazar, G. C. and Sar¬göl M. A., On factor relations between weighted and Nörlund means,Tamkang J. Math. (in press)[8] Kogbetliantz, E., Sur lesseries absolument sommables par la methods des moyannes arith-metiques, Bull. des Sci. Math. 49 (1925), 234-256.[9] Maddox, I.J., Elements of functinal analysis, Cambridge University Press, London, NewYork, (1970).[10] Mazhar, S.M., On the absolute summability factors of in…nite series, Tohoku Math. J.,23(1971), 433-451.[11] Mehdi, M.R., Summability factors for generalized absolute summability I, Proc. LondonMath. Soc.(3), 10 (1960), 180-199.[12] Mohapatra, R. N., On absolute Riesz summability factors, J. Indian Math. Soc. 32(1968),113-129.[13] Orhan, C. and Sar¬göl, On absolute weighted mean summability, Rocky Mount. J. Math.23 (1993), 1091-1097.[14] Sarıgöl, M.A., Spaces of series Summable by absolute Cesàro and Matrix Operators ,Comm. Math. Appl. 7(1), (2016), 11-22.[15] Sarıgöl, M.A., Extension of Mazhar’s theorem on summability factors, Kuwait J. Sci. 42(3) (2015), 28-35.[16] Sarıgöl, M.A., On the local properties of factored Fourier series, Appl. Math. Comp., 216(2010), 3386-3390.[17] Sarıgöl, M.A., and Bor, H., Characterization of absolute summability factors, J. Math.Anal. Appl. 195 (1995), 537-545.[18] Sarıgöl, M.A., On two absolute Riesz summability factors of in…nite series, Proc. Amer.Math. Soc. 118 (1993), 485-488.[19] Sarıgöl, M.A., A note on summability, Studia Sci. Math. Hungar. 28 (1993), 395-400.[20] Sulaiman, W.T., On summability factors of in…nite series, Proc. Amer. Math. Soc. 115(1992), 313-317.[21] Sulaiman, W.T., On some absolute summability factors of In…nite Series, Gen. Math.Notes, 2 (2) (2011), 7-13.[22] Thorpe, B., Matrix transformations of Cesàro summable Series, Acta Math. Hung., 48(3-4), (1986), 255-265.
Toplam 1 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

G. Canan Hazar Güleç 0000-0002-8825-5555

Yayımlanma Tarihi 1 Aralık 2018
Gönderilme Tarihi 15 Ekim 2018
Kabul Tarihi 12 Kasım 2018
Yayımlandığı Sayı Yıl 2018

Kaynak Göster

APA Hazar Güleç, G. C. (2018). Summability factors between the absolute Cesàro methods. Sakarya University Journal of Science, 22(6), 1923-1926. https://doi.org/10.16984/saufenbilder.470493
AMA Hazar Güleç GC. Summability factors between the absolute Cesàro methods. SAUJS. Aralık 2018;22(6):1923-1926. doi:10.16984/saufenbilder.470493
Chicago Hazar Güleç, G. Canan. “Summability Factors Between the Absolute Cesàro Methods”. Sakarya University Journal of Science 22, sy. 6 (Aralık 2018): 1923-26. https://doi.org/10.16984/saufenbilder.470493.
EndNote Hazar Güleç GC (01 Aralık 2018) Summability factors between the absolute Cesàro methods. Sakarya University Journal of Science 22 6 1923–1926.
IEEE G. C. Hazar Güleç, “Summability factors between the absolute Cesàro methods”, SAUJS, c. 22, sy. 6, ss. 1923–1926, 2018, doi: 10.16984/saufenbilder.470493.
ISNAD Hazar Güleç, G. Canan. “Summability Factors Between the Absolute Cesàro Methods”. Sakarya University Journal of Science 22/6 (Aralık 2018), 1923-1926. https://doi.org/10.16984/saufenbilder.470493.
JAMA Hazar Güleç GC. Summability factors between the absolute Cesàro methods. SAUJS. 2018;22:1923–1926.
MLA Hazar Güleç, G. Canan. “Summability Factors Between the Absolute Cesàro Methods”. Sakarya University Journal of Science, c. 22, sy. 6, 2018, ss. 1923-6, doi:10.16984/saufenbilder.470493.
Vancouver Hazar Güleç GC. Summability factors between the absolute Cesàro methods. SAUJS. 2018;22(6):1923-6.

30930 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.