ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS

The sequence space βVa was introduced and studied by Mursaleen [9]. In this paper we extend βVa to βVa M,p,r and study some properties and inclusion relations on this space.

___

  • Z.U. Ahmad and M. Mursaleen , An application of banach limits, Proc. Amer. Math.Soc. 103 (1983), 244 - 246.
  • S.T. Chen, Geometry of Orlicz Spaces, Dissertationes Math. (The Institute of Mathematics, Polish Academy of Sciences) (1996).
  • M. A. Krasnoselskii, and Rutickii, Ya. B, Convex Functions and Orlicz Spaces, (Gooningen: P. Nordho Ltd.) (1961) (translation).
  • J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces,Israel J. Math., : 379-390 (1971).
  • G.G. Lorentz, A contribution to the theory of divergent series, Acta Math. (1948) 167-190.
  • W. A. Luxemburg, Banach Function Spaces, Thesis (Delft) (1955)
  • L. Maligranda, Orlicz spaces and interpolation, Seminar in Math. 5, Camp- inas (1989)
  • M.Mursaleen , Matrix transformations between some new sequence spaces, Houston J. Math., 9 (1983), 505- 509.
  • M.Mursaleen ,On some new invariant matrix methods of summability, Quart. J. Math., Oxford (2) 34 (1983), 77-86 .
  • J. Musielak , Orlicz Spaces and Modular spaces, Lecture Notes in Math. (Springer- Verlag) (1983).
  • W. Orlicz, Ü ber Raume(O ), Bulletin International de l’ Académie Polon- aise des Sciences et des Letters, Série A, 93 - 107 (1936).
  • R. A. Raimi, Invariant means and invariant matrix method of summability, Duke Math. J. ., 30 (1963), 81- 94.
  • M. M . Rao and Z. D. Ren, Theory of Orlicz spaces (New York, Basel, Hong Kong: Marcel Dekker Inc.) (1991).
  • P. Schafer , InŞnite matrices and invariant means, Proc. Amer. Math.Soc. (1972), 104 - 110.
  • A. Wilansky, Summability Through Functional Analysis, North-Holland Mathematical Studies 85, 1984.
  • Current address : Department of Mathematics, A. M. U. Aligarh-202002 INDIA
  • E-mail address :vakhan@math.com
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics-Cover
  • ISSN: 1303-5991
  • Yayın Aralığı: Yılda 4 Sayı
  • Başlangıç: 1948
  • Yayıncı: Ankara Üniversitesi