On Some Lacunary Generalized Difference Sequence Spaces of Invariant Means De ned by a Sequence of Modulus Function

• Journal title : Kyungpook mathematical journal
• Volume 51, Issue 4,  2011, pp.385-393
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2011.51.4.385
Title & Authors
On Some Lacunary Generalized Difference Sequence Spaces of Invariant Means De ned by a Sequence of Modulus Function
Atici, Gulcan; Bektas, Cigdem Asma;

Abstract
The aim of this paper is to introduce and study the sequence spaces [w, $\small{{\theta}}$, F, p, q]$\small{_{\infty}({\Delta}_{\upsilon}^m)}$, [w, $\small{{\theta}}$, F, p, q]$\small{_1({\Delta}_{\upsilon}^m)}$ and [w, $\small{{\theta}}$, F, p, q]$\small{_0({\Delta}_{\upsilon}^m)}$, which arise from the notions of generalized difference sequence space, lacunary convergence, invariant mean and a sequence of Moduli $F Keywords Invariant mean;Difference sequence spaces;lacunary sequence;modulus function; Language English Cited by References 1. R. Wisbauer, Foundations of module and ring theory, Gordon and Beach Science Publishers, 1991. 2. C. A. Bektas and R. Colak, Generalized difference sequences defined by a sequence of moduli, Soochow J. Math., 29(2)(2003), 215-220. 3. C. A. Bektas and R. Colak, Generalized strongly almost summable difference sequences of order m de ned by a sequence of moduli, Demonstratio Mathematica, 40(3)(2007), 581-591. 4. M. Et, Spaces of Cesaro difference sequences of order r defined by a Modulus function in a locally convex space, Taiwanese Journal of Mathematics, 10(4)(2006), 865-879. 5. M. Et, Y. Altin, B. Choudhary and B. C. Tripathy, On some classes of sequences de ned by sequences of Orlicz functions, Mathematical Inequalities and Applications, 9(2)(2006), 335-342. 6. M. Et and R. Colak, On some generalized difference sequence spaces, Soochow J. Math., 21(1995), 377-386. 7. M. Et and A. Esi, On Kothe-Toeplitz duals of generalized difference sequence spaces, Bull. Malaysian Math. Sc. Soc., 23(2)(2000), 25-32. 8. M. Et and A. Gokhan, Lacunary strongly almost summable sequences, Studia Univ. Babes-Bolyai Mathematica, 4(2008), 29-38. 9. A. R. Freedman, J. J. Sember and M. Raphael, Some Ces'aro-type summability spaces, Proc. London Math. Soc., 37(3)(1978), 508-520. 10. H. Kzmaz, On certain sequence spaces, Canad. Math. Bull., 24(1981), 169-176. 11. G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math., 80(1948), 167-190. 12. I. J. Maddox, Elements of Functional Analysis. Cambridge University Press, Cambridge, London and New York, 1970. 13. I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Cambridge Philos. Soc., 100(1986), 161-166. 14. S. Pehlivan and B. Fisher, Lacunary strong convergence with respect to a sequence of modulus functions, Comment Math. Univ. Carolin, 36(1995), 69-76. 15. W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25(1973), 973-978. 16. P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36(1972), 104-110. 17. B. C. Tripathy and M. Sen, On generalized statistically convergent sequences, Indian Journal of Pure and Applied Mathematics, 32(11)(2001), 1689-1694. 18. B. C. Tripathy, On generalized difference paranormed statistically convergent sequences, Indian Journal of Pure and Applied Mathematics, 35(5)(2004), 655-663. 19. B. C. Tripathy and S. Mahanta, On a class of generalized lacunary difference sequence spaces defined by Orlicz function, Acta Mathematica Applicata Sinica, 20(2)(2004), 231-238. 20. B. C. Triapthy and S. Mahanta, On a class of vector valued sequences associated with multiplier sequences, Acta Mathematica Applicata Sinica, 20(3)(2004), 487-494. 21. B. C. Tripathy and M. Sen, Characterization of some matrix classes involving para- normed sequence spaces, Tamkang Journal of Mathematics, 37(2)(2006), 155-162. 22. B. C. Tripathy and B. Sarma, Statistically convergent difference double sequence spaces, Acta Mathematica Sinica, 24(5)(2008), 737-742. 23. B. C. Tripathy, Y. Altin and M. Et, Generalized difference sequences spaces on seminormed spaces defined by Orlicz functions, Mathematica Slovaca, 58(3)(2008), 315-324. 24. B. C. Tripathy and S. Borgohain, Difference sequence space$m(M,{\phi},{\Delta}^n_m,p)^F\$ of fuzzy real numbers, Mathematical Modelling and Analysis, 13(4)(2008), 577-586.

25.
B. C. Tripathy, B. Choudhary and B. Sarma, On some new type generalized difference sequence spaces, Kyungpook Math. J., 48(4)(2008), 613-622.

26.
B. C. Tripathy and B. Sarma, Vector valued double sequence spaces defined by Orlicz function, Mathematica Slovaca, 59(6)(2009), 767-776.

27.
B. C. Tripathy and A. Baruah, New type of difference sequence spaces of fuzzy real numbers, Mathematical Modelling and Analysis, 14(3)(2009), 391-397.

28.
B. C. Tripathy and H. Dutta, On some new paranormed difference sequence spaces defined by Orlicz functions, Kyungpook Math. J., 50(2010), 59-69.

29.
A. Wilansky, Functional Analysis, Blaisdell Publishing Company, New York, 1964.