ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS

A. Khan Vakeel

ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS

Year 2008, Volume: 57 Issue: 2, 25 - 33, 01.08.2008

Abstract

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.

Keywords

Invariant mean, Paranorm, Orlicz function, Solid space

References

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

Year 2008, Volume: 57 Issue: 2, 25 - 33, 01.08.2008

A. Khan Vakeel

Abstract

References

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

There are 17 citations in total.

Details

Primary Language	English
Journal Section	Research Articles
Authors	A. Khan Vakeel This is me
Publication Date	August 1, 2008
Published in Issue	Year 2008 Volume: 57 Issue: 2

Cite

APA	Khan Vakeel, A. (2008). ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 57(2), 25-33.
AMA	Khan Vakeel A. ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2008;57(2):25-33.
Chicago	Khan Vakeel, A. “ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 57, no. 2 (August 2008): 25-33.
EndNote	Khan Vakeel A (August 1, 2008) ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 57 2 25–33.
IEEE	A. Khan Vakeel, “ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 57, no. 2, pp. 25–33, 2008.
ISNAD	Khan Vakeel, A. “ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 57/2 (August 2008), 25-33.
JAMA	Khan Vakeel A. ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2008;57:25–33.
MLA	Khan Vakeel, A. “ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 57, no. 2, 2008, pp. 25-33.
Vancouver	Khan Vakeel A. ON A NEW SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2008;57(2):25-33.