Some classes of almost convergent paranormed sequence spaces defined by Orlicz functions

• Autorzy: Isik M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we define (...), the sequence spaces on a seminormed complex linear space, using an Orlicz function. We give various properties and some inclusion relations on this space.

Słowa kluczowe

EN

Orlicz function; invariant mean; seminorm

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2012
• Tom: Vol. 45, nr 3
• Strony: 585--592
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Isik M.

• Department Of Statistics Firat University 23119, Elazig, Turkey,

Bibliografia

• [1] Z. U. Ahmad, M. Mursaleen, An application of Banach limits, Proc. Amer. Math. Soc. 103 (1988), 244–246.
• [2] Y. Altin, M. Et, B. C. Tripathy, The sequence space | ¯Np|(M, r, q, s) on seminormed spaces, Appl. Math. Comput. 154 (2004), 423–430.
• [3] Y. Altin, Properties of some sets of sequences defined by a modulus function, Acta Math. Sci. (English Ed.) 29 (2009), 427–434.
• [4] S. Banach, Theorie des Operations Linearies, Warszawa, 1932.
• [5] B. Choudhary, S. D. Parashar, A sequence space defined by Orlicz functions, Approx. Theory Appl. (N.S.) 18(4) (2002), 70–75.
• [6] M. Et, Y. Altin, B. Choudhary, B. C. Tripathy, On some classes of sequences defined by sequences of Orlicz functions, Math. Inequal. Appl. 9 (2006), 335–342.
• [7] V. A. Khan, On Riesz–Musielak–Orlicz sequence spaces, Numer. Funct. Anal. Optim. 2
• [8] P. K. Kamthan, M. Gupta, Sequence Spaces and Series, Lecture Notes in Pure and Applied Mathematics, 65, Marcel Dekker Inc., New York, 1981.
• [9] M. A. Krasnoselskii, Y. B. Rutickii, Convex Functions and Orlicz Spaces, Groningen, Netherlands, 1961.
• [10] J. Lindenstrauss, L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 10 (1971), 379–390.
• [11] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190.
• [12] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. ( Oxford 2nd Ser.) 18(72) (1967), 345–355.
• [13] M. Mursaleen, On some new invariant matrix methods of summability, Quart. J. Math. Oxford 34(2) (1983), 77–86.
• [14] M. Mursaleen, Matrix transformations between some new sequence spaces, Houston J. Math. 9 (1983), 505–509.
• [15] M. Mursaleen, Q. A. Khan, T. A. Chishti, Some new convergent sequences defined by Orlicz functions and statistical convergence, Ital. J. Pure Appl. Math. 9 (2001), 25–32.
• [16] W. Orlicz, Über Räume (LM), Bull. Int. Acad. Polon. Sci. A (1936), 93–107.
• [17] R. A. Raimi, Invariant means and invariant matrix method of summability, Duke Math. J. 30 (1963), 81–94.
• [18] P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36 (1972), 104–110.
• [19] P. D. Srivastava, Ghosh, K. Dalim, On vector valued sequence spaces hN(Ek), ℓM(B(Ek, Y )) and ℓM(E′k)), J. Math. Anal. Appl. 327 (2007), 1029–1040.
• [20] B. C. Tripathy, S. Mahanta, On a class of sequences related to the ℓp spaces defined by Orlicz function, Soochow J. Math. 29 (2003), 379–391.
• [21] B. C. Tripathy, S. Mahanta, On a class of generalized lacunary difference sequence spaces defined by Orlicz functions, Acta Math. Appl. Sinica (English Ser.) 20 (2004), 231–238.
• [22] B. C. Tripathy, M. Sen, Characterization of some matrix classes involving paranormed sequence spaces, Tamkang J. Math. 37 (2006), 155–162.
• [23] B. C. Tripathy, Y. Altin, M. Et, Generalized difference sequence spaces on seminormed space defined by Orlicz functions, Math. Slovaca 58 (2008), 315–324.
• [24] B. C. Tripathy, B. Sarma, Sequence spaces of Fuzzy real numbers defined by Orlicz functions, Math. Slovaca 58 (2008), 621–628.
• [25] B. C. Tripathy, H. Dutta, On some new paranormed difference sequence spaces defined by Orlicz functions, Kyungpook Math. J. 50 (2010), 59–69.
• [26] B. C. Tripathy, B. Sarma, Vector valued double sequence spaces defined by Orlicz function, Math. Slovaca 59 (2009), 767–776.
• [27] A. Wilansky, Functional Analysis, Blaisdell Publishing Company, New York, 1964.