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On a study of double gai sequence space

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let χ2 denote the space of all prime sense double gai sequences and Λ2 the space of all prime sense double analytic sequences. This paper is devoted to the general properties of χ2.
Rocznik
Tom
Strony
95--111
Opis fizyczny
Bibliogr. 45 poz.
Twórcy
  • Department of Mathematics, SASTRA University, Thanjavur-613 401, India.
autor
  • Department of Mathematics, SASTRA University, Thanjavur-613 401, India.
Bibliografia
  • [1] T.Apostol, Mathematical Analysis, Addison-Wesley, London, 1978.
  • [2] M.Basarir and O.Solancan, On some double sequence spaces, J. Indian Acad.Math., 21(2) (1999), 193-200.
  • [3] C.Bektas and Y.Altin, The sequence space lM (p,q,s) on seminormed spaces, Indian J. Pure Appl. Math., 34(4) (2003), 529-534.
  • [4] T.J.I'A.Bromwich, An introduction to the theory of in nite series Macmillan and Co.Ltd., New York, (1965).
  • [5] J.C.Burkill and H.Burkill, A Second Course in Mathematical Analysis Cambridge University Press, Cambridge, New York, (1980).
  • [6] R.Colak and A.Turkmenoglu, The double sequence spaces l2∞(p), c20(p) and c2(p), (to appear).
  • [7] M.Gupta and P.K.Kamthan,Infinite matrices and tensorial transformations, Acta Math., Vietnam 5 (1980), 33-42.
  • [8] G.H.Hardy, On the convergence of certain multiple series, Proc. Camb. Phil. Soc., 19 (1917), 86-95.
  • [9] M.A.Krasnoselskii and Y.B.Rutickii, Convex functions and Orlicz spaces, Gorningen, Netherlands, 1961.
  • [10] J.Lindenstrauss and L.Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379-390.
  • [11] I.J.Maddox, Sequence spaces defined by a modulus, Math. Proc. Cambridge Philos. Soc, 100(1) (1986), 161-166.
  • [12] F.Moricz, Extentions of the spaces c and c0 from single to double sequences, Acta. Math. Hungerica, 57(1-2), (1991), 129-136.
  • [13] F.Moricz and B.E.Rhoades, Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Phil. Soc., 104, (1988), 283-294.
  • [14] M.Mursaleen, M.A.Khan and Qamaruddin, Difference sequence spaces defined by Orlicz functions, Demonstratio Math. , Vol. XXXII (1999), 145-150.
  • [15] H.Nakano, Concave modulars, J. Math. Soc. Japan, 5(1953), 29-49.
  • [16] W.Orlicz, Über Raume (LM) Bull. Int. Acad. Polon. Sci. A, (1936), 93-107.
  • [17] S.D.Parashar and B.Choudhary, Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math., 25(4)(1994), 419-428.
  • [18] K.Chandrasekhara Rao and N.Subramanian, The Orlicz space of entire sequences, Int. J. Math. Math. Sci., 68(2004), 3755-3764.
  • [19] W.H.Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25(1973), 973-978.
  • [20] B.C.Tripathy, On statistically convergent double sequences, Tamkang J. Math., 34(3), (2003), 231-237.
  • [21] B.C.Tripathy,M.Et and Y.Altin, Generalized difference sequence spaces defined by Orlicz function in a locally convex space, J. Analysis and Applications, 1(3)(2003), 175-192.
  • [22] A.Turkmenoglu, Matrix transformation between some classes of double sequences, Jour. Inst. of math. and Comp. Sci. (ath. Seri.), 12(1), (1999), 23-31.
  • [23] A.Wilansky, Summability through Functional Analysis, North-Holland Mathematics Studies, North-Holland Publishing, Amsterdam, Vol.85(1984).
  • [24] P.K.Kamthan and M.Gupta, Sequence spaces and series, Lecture notes, Pure and Applied Mathematics, 65 Marcel Dekker, Inc., New York , 1981.
  • [25] M.Gupta and P.K.Kamthan, Infinite Matrices and tensorial transformations, Acta Math. Vietnam 5, (1980), 33-42.
  • [26] N.Subramanian, R.Nallswamy and N.Saivaraju, Characterization of entire sequences via double Orlicz space, Internaional Journal of Mathematics and Mathemaical Sciences, Vol.2007(2007), Article ID 59681, 10 pages.
  • [27] A.Gökhan and R.Colak, The double sequence spaces cP2(p) and cPB2(p), Appl. Math. Comput., 157(2), (2004), 491-501.
  • [28] A.Gökhan and R.Colak, Double sequence spaces l∞2, ibid., 160(1), (2005), 147-153.
  • [29] M.Zeltser, Investigation of Double Sequence Spaces by Soft and Hard Analitical Methods, Dissertationes Mathematicae Universitatis Tartuensis 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, Tartu, 2001.
  • [30] M.Mursaleen and O.H.H. Edely, Statistical convergence of double sequences, J.Math. Anal. Appl., 288(1), (2003), 223-231.
  • [31] M.Mursaleen, Almost strongly regular matrices and a core theorem for double sequences, J. Math. Anal. Appl., 293(2), (2004), 523-531.
  • [32] M.Mursaleen and O.H.H. Edely, Almost convergence and a core theorem for double sequences, J. Math. Anal. Appl., 293(2), (2004), 532-540.
  • [33] B.Altay and F.Basar, Some new spaces of double sequences, J. Math. Anal. Appl., 309(1), (2005), 70-90.
  • [34] F.Basar and Y.Sever, The space Lp of double sequences, Math. J. Okayama Univ, 51, (2009), 149-157.
  • [35] N.Subramanian and U.K.Misra, The semi normed space defined by a double gai sequence of modulus function, Fasciculi Math., 46, (2010).
  • [36] H.Kizmaz, On certain sequence spaces, Cand. Math. Bull., 24(2), (1981), 169-176.
  • [37] N.Subramanian and U.K.Misra, Characterization of gai sequences via double Orlicz space, Southeast Asian Bulletin of Mathematics, (revised).
  • [38] N.Subramanian, B.C.Tripathy and C.Murugesan, The double sequence space of Γ2, Fasciculi Math., 40, (2008), 91-103.
  • [39] N.Subramanian, B.C.Tripathy and C.Murugesan, The Cesáro of double entire sequences, International Mathematical Forum, 4 no.2(2009), 49-59.
  • [40] N.Subramanian and U.K.Misra, The Generalized double of gai sequence spaces, Fasciculi Math., 43, (2010).
  • [41] N.Subramanian and U.K.Misra, Tensorial transformations of double gai sequence spaces, International Journal of Computational and Mathematical Sciences, 3:4, (2009), 186-188.
  • [42] Erwin Kreyszig, Introductory Functional Analysis with Applications, by John Wiley and Sons Inc. , 1978.
  • [43] M.Mursaleen and S.A.Mohiuddine, Regularly σ-conservative and σ-coercive four dimensional matrices, Computers and Mathematics with Applications, 56(2008), 1580-1586.
  • [44] M.Mursaleen and S.A.Mohiuddine, On σ-conservative and boundedly σ-conservative four dimensional matrices, Computers and Mathematics with Applications, 59(2010), 880-885.
  • [45] M.Mursaleen and S.A.Mohiuddine, Double σ-multiplicative matrices, J. Math. Anal. Appl., 327(2007), 991-996.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-88298ad7-74a9-4df8-9efc-0f3f7601fd14
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