Yıl 2017, Cilt 5, Sayı 2, Sayfalar 260 - 267 2017-10-15
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## DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES

#### RAMAZAN KAMA [1] , BİLAL ALTAY [2]

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In this paper we show that completeness and barrelledness of a normed space can be characterized by means of sequence spaces obtained by a sequence in a normed space and difference matrix method. Other related results are established.

Difference sequence spaces, weakly unconditionally Cauchy series, completeness, barrelled
• [1] Aizpuru, A. and Perez-Fernandez, F. J., Characterizations of series in Banach spaces, Acta Math. Univ. Comenian., 58 (1999), No. 2, 337–344.
• [2] Aizpuru, A. and Perez-Fernandez, F. J., Sequence spaces associated to a series in a Banach space (sequence spaces associated to a series), Indian J. pure appl. Math., 33 (2002), No. 9, 1317–1329.
• [3] F.Albiac, N. J.Kalton, Topics in Banach Spaces Theory, Springer-Verlag, New York (2006).
• [4] B. Altay, F. Basar Certain topological properties and duals of the domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336 (2007), no. 2, 632–645.
• [5] F. Basar, B. Altay, On the space of sequences of p-bounded variation and related matrix mappings, (English, Ukrainian summary) Ukrain. Mat. Zh., 55(1) (2003), 108–118; reprinted in Ukrainian Math. J., 55(1) (2003), 136–147.
• [6] C.A. Bektas, R. Colak, On some generalized difference sequence spaces, Thai J. Math., 3(1) (2005), 83–98.
• [7] C. Bessaga, A. Pelczynski, On bases and unconditional convergence of series in Banach spaces, Stud. Math., 17 (1958), 151–164.
• [8] J. Diestel, Sequences and Series in Banach Spaces, Springer-Verlag, New York (1984).
• [9] M. Et and R. Colak, On some generalized difference sequence spaces, Soochow J. of Math., 21(4) (1995), 377–386.
• [10] R. Kama, B. Altay, F. Basar, On the domains of backward difference matrix and the spaces of convergence of a series, preprint.
• [11] R. Kama, B. Altay, Some sequence spaces and completeness of normed spaces, Creat. Math. Inform., to appear.
• [12] V. Karakaya, E. Sava ̧s, H. Polat, Some paranormed Euler sequence spaces of difference sequences of order m, Mathematica Slovaca, 63(4) (2013), 849–862.
• [13] H. Kızmaz, On certain sequence spaces, Canad. Math. Bull., 24(2) (1981), 169–175.
• [14] E. Malkowsky, Mursaleen and Qamaruddin, Generalized sets of difference sequences, their duals and matrix transformations, Advances in Sequence Spaces and Applications, Narosa, New Delhi, (1999), 68-83.
• [15] C.W. McArthur, On relationships amongst certain spaces of sequences in an arbitrary Banach space, Canad. J. Math., 8 (1956), 192–197.
• [16] F.J. Perez-Fernandez, F. Benıtez-Trujillo, A. Aizpuru, Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series, Czechoslovak Math. J., 50 (2000), no. 125, 889–896.
Konular Mühendislik Articles Yazar: RAMAZAN KAMAÜlke: Turkey Yazar: BİLAL ALTAYÜlke: Turkey
 Bibtex @araştırma makalesi { konuralpjournalmath310582, journal = {Konuralp Journal of Mathematics}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {2017}, volume = {5}, pages = {260 - 267}, doi = {}, title = {DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES}, key = {cite}, author = {KAMA, RAMAZAN and ALTAY, BİLAL} } APA KAMA, R , ALTAY, B . (2017). DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES. Konuralp Journal of Mathematics, 5 (2), 260-267. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/28490/310582 MLA KAMA, R , ALTAY, B . "DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES". Konuralp Journal of Mathematics 5 (2017): 260-267 Chicago KAMA, R , ALTAY, B . "DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES". Konuralp Journal of Mathematics 5 (2017): 260-267 RIS TY - JOUR T1 - DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES AU - RAMAZAN KAMA , BİLAL ALTAY Y1 - 2017 PY - 2017 N1 - DO - T2 - Konuralp Journal of Mathematics JF - Journal JO - JOR SP - 260 EP - 267 VL - 5 IS - 2 SN - -2147-625X M3 - UR - Y2 - 2017 ER - EndNote %0 Konuralp Journal of Mathematics DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES %A RAMAZAN KAMA , BİLAL ALTAY %T DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES %D 2017 %J Konuralp Journal of Mathematics %P -2147-625X %V 5 %N 2 %R %U ISNAD KAMA, RAMAZAN , ALTAY, BİLAL . "DIFFERENCE MATRIX AND SOME MULTIPLIER SEQUENCE SPACES". Konuralp Journal of Mathematics 5 / 2 (Ekim 2017): 260-267.