Statistical convergence on composite vector valued sequence space

• Autorzy: Basu A. , Srivastava P. D.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we have defined the idea of statistical convergence and statistically Cauchy sequence over the generalized class of composite vector valued sequence space F(Ek, f). The class F(Ek, f) is in-troduced and discussed by Ghosh and Srivastava [7], where F is a normal paranormed sequence space, Ek's are Banach spaces and f is a modulus function. We have established some results of Fridy, Connor and Rath and Tripathy, such as, decomposition of statistically convergent sequences, equivalence of statistical convergence and statistical Cauchy convergence and sequentially completeness of the space of bounded statistically con-vergent sequences of F [E, f].

Słowa kluczowe

EN

statistical convergence; density function; modulus function; paranorm; composite vector valued sequence space

PL

konvergencja statystyczna; funkcja gęstości; wektor złożony; przestrzeń ciągu

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2007
• Tom: Vol. 29
• Strony: 75--90
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Basu A.

autor

Srivastava P. D.

• Department of Mathematics Indian Institute of Technology Kharagpur, Kharagpur-721302,

Bibliografia

• [1] Buck, R. C., Generalized asymptotic density, Amer. Jour. Math, 75 (1953), 335-346.
• [2] Bilgin, T., The Sequence Space l(p,fv,q,s), Journal of Faculty of Education, 1(1), (1994), 73-82.
• [3] Connor, J., The statistical and strong p-Cesaro convergence of sequence, Analysis, 8 (1988), 47-63.
• [4] Fast, H., Sur la convergence statistique, Colloq. Math, 2 (1951), 241-244.
• [5] Freedman, A. R. and Sember, J. J., Densities and Summability, Pacific Jour. of Math., 85(2) (1981), 293-305.
• [6] Fridy, J. A., On statitical convergence, Analysis, 5 (1985), 301-313.
• [7] Ghosh, D. and Srivastava P. D., On some vector valued seąuence spaces defined using a rnodulus function Indian J. Pure Appl. Math, 30(8) (1999), 819-826.
• [8] Maddox, I. J., Infinite Matrices of Operators, Lecture Notes in Mathematics, Springer-Yerlag Berlin, New york, 1980.
• [9] Maddox,I. J., Sequence spaces defined by a modulus , Proc. Camb. Phil. Soc. 100, (1986), 161-166.
• [10] Maddox,I. J., Statistical convergence in a locally convex space, Math. Proc. Camb. Phil. Soc., 104 (1988), 141-145.
• [11] Özturk, E., Bilgin, T.: Strongly summable seąuence spaces Defined By a Modulus, Indian J. Pure Appl. Math., 25 (6), (2004), 621-625.
• [12] Rath, D. and Tripathy, B. C., On statistically convergent and statistically Cauchy sequences, Indian Jour. Pure Appl. Math, 25(4) (1994), 381-386.
• [13] Ruckle, W., FK spaces in which the seąuence of co-ordinate vectors is bounded, Cand. J. Math. 25 (1973), 973-978.
• [14] Salat, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139-150.
• [15] Schoenberg, I. J., The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361-375.
• [16] Tripathy, B. C., Proc. Estonian Acad. Sci. Phys. Math, 47(4) (1998), 299-303.
• [17] Niven, L, Zuckerman, H. S., Montogomery, H. L., An Introduction To The Theory of Numbers, John Wiley & Sons Inc. New York., 1960.