Yıl 2018, Cilt 22, Sayı 6, Sayfalar 1923 - 1926 2018-12-01
| | | |

## Summability factors between the absolute Cesàro methods

#### G. Canan Hazar Güleç [1]

##### 19 44

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&gt;1 and (|C,-1|,|C,α|_{k}) , k≥1 for α&gt;-1. Also, in the special case, we give some inclusion relations between methods, which completes some open problems in literature.
Sequence spaces, Absolute Cesàro summability, Summability Factors
• [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.
Birincil Dil en Matematik December 2018 Araştırma Makalesi Orcid: 0000-0002-8825-5555Yazar: G. Canan Hazar GüleçKurum: PAMUKKALE UNIVERSITYÜlke: Turkey
 Bibtex @araştırma makalesi { saufenbilder470493, journal = {Sakarya University Journal of Science}, issn = {1301-4048}, eissn = {2147-835X}, address = {Sakarya Üniversitesi}, year = {2018}, volume = {22}, pages = {1923 - 1926}, doi = {10.16984/saufenbilder.470493}, title = {Summability factors between the absolute Cesàro methods}, key = {cite}, author = {Hazar Güleç, G. Canan} } APA Hazar Güleç, G . (2018). Summability factors between the absolute Cesàro methods. Sakarya University Journal of Science, 22 (6), 1923-1926. DOI: 10.16984/saufenbilder.470493 MLA Hazar Güleç, G . "Summability factors between the absolute Cesàro methods". Sakarya University Journal of Science 22 (2018): 1923-1926 Chicago Hazar Güleç, G . "Summability factors between the absolute Cesàro methods". Sakarya University Journal of Science 22 (2018): 1923-1926 RIS TY - JOUR T1 - Summability factors between the absolute Cesàro methods AU - G. Canan Hazar Güleç Y1 - 2018 PY - 2018 N1 - doi: 10.16984/saufenbilder.470493 DO - 10.16984/saufenbilder.470493 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 1923 EP - 1926 VL - 22 IS - 6 SN - 1301-4048-2147-835X M3 - doi: 10.16984/saufenbilder.470493 UR - http://dx.doi.org/10.16984/saufenbilder.470493 Y2 - 2018 ER - EndNote %0 Sakarya University Journal of Science Summability factors between the absolute Cesàro methods %A G. Canan Hazar Güleç %T Summability factors between the absolute Cesàro methods %D 2018 %J Sakarya University Journal of Science %P 1301-4048-2147-835X %V 22 %N 6 %R doi: 10.16984/saufenbilder.470493 %U 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. http://dx.doi.org/10.16984/saufenbilder.470493