Strong invariant A-summability with respect to a sequence of modulus functions in seminormed space

• Autorzy: Bhardwaj V. , Bala I.
• Języki publikacji: EN

Abstrakty

EN

The object of this paper is to introduce some new strongly invariant A-summable sequence spaces defined by a sequence of modulus functions T = (fk) in a seminormed space, when A = (ank) is a non-negative regular matrix. Various algebraic and topological properties of these spaces, and some inclusion relations between these spaces have been discussed. Finally, we study some relations between ^4-invariant statisti-cal convergence and strong invariant A-summability with respect to a seąuence of modulus functions in a seminormed space.

Słowa kluczowe

EN

sequence space; invariant mean; modulus function; statistical convergence

PL

przestrzeń ciągu; wartość niezmiennika; funkcja modułowa; zbieżność statystyczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 4
• Strony: 869--877
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Bhardwaj V.

autor

Bala I.

• Department of Mathematics Kurukshetra University Kurukshetra-136 119, India,

Bibliografia

• [1] Y. Altin and M. Isik, On some new seminormed sequence spaces defined by modulus functions, Hokkaido Math. J. 35 (2006), 565-572.
• [2] S. Banach, Theorie des Operations Lin ́earies, Warszawa, 1932.
• [3] R. Colak, B. C. Tripathy and M. Et, Lacunary strongly summable sequences and q-lacunary almost statistical convergence, Vietnam J. Math. 34(2) (2006), 129-138.
• [4] J. S. Connor, The statistical and strong p-Ces`aro convergence of sequences, Analysis 8 (1988), 47-63.
• [5] R. G. Cooke, Infinite Matrices and Sequence Spaces, Macmillan and Co., London 1950.
• [6] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
• [7] A. R. Freedman, J. J. Sember and M. Raphael, Some Ces`aro type summability spaces, Proc. London Math. Soc. 37 (3) (1978), 508-520.
• [8] A. R. Freedman and J. J. Sember, Densities and summability, Pacific J. Math. 95 (1981), 293-305.
• [9] J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301-313.
• [10] E. Kolk, The statistical convergence in Banach spaces, Acta Comment. Univ. Tartu. 928 (1991), 41-52.
• [11] E. Kolk, On strong boundedness and summability with respect to a sequence of moduli, Tartu Ul. Toimetised 960 (1993), 41-50.
• [12] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190.
• [13] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford 18 (2) (1967), 345-355.
• [14] I. J. Maddox, A new type of convergence, Math. Proc. Camb. Philos. Soc. 83 (1978), 61-64.
• [15] I. J. Maddox, On strong almost convergence, Math. Proc. Camb. Philos. Soc. 85 (1979), 345-350.
• [16] I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Philos. Soc. 100 (1986), 161-166.
• [17] I. J. Maddox, Statistical convergence in a locally convex space, Math. Proc. Camb. Philos. Soc. 104 (1988), 141-145.
• [18] Mursaleen, On some new invariant matrix methods of summability, Quart. J. Math. Oxford 34 (1983), 77-86.
• [19] Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math. 9 (1983), 505-509.
• [20] F. Nuray and E. Savas, Invariant statistical convergence and A-invariant statistical convergence, Indian J. Pure Appl. Math. 25(3) (1994), 267-274.
• [21] S. Pehlivan and B. Fisher, On some sequence spaces, Indian J. Pure Appl. Math. 25 (10) (1994), 1067-1071.
• [22] S. Pehliyan and B. Fisher, Lacunary strong convergence with respect to a sequence of modulus functions, Comment. Math. Univ. Carolinae 36 (1) (1995), 69-76.
• [23] W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math. 25 (1973), 973-978.
• [24] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (2) (1980), 139-150.
• [25] E. Savas, Strongly σ-convergent sequences, Bull. Calcutta Math. Soc. 81 (4) (1989), 295-300.
• [26] P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36 (1972), 104-110.
• [27] A. Wilansky, Functional Analysis, Blaisdell Publishing Company, New York, 1964.