SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION

Yıl 2016, Cilt: 4 Sayı: 2, 169 - 176, 01.10.2016

SELMA Altundag MERVE Abay

Öz

We introduce basic properties of some sequence spaces using ideal convergent and Musielak Orlicz function $\mathcal{M}=(M_k)$. Including relations related to these spaces are investigated in this paper.

Anahtar Kelimeler

Ideal, $\mathcal{I}$-convergence, paranorm space, Musielak-Orlicz function

Kaynakça

• [1] P. Kostyrko, T. Salat, W. Wilczynski, I-convergence, Real Anal. Exchange 262, (2000), 669-685, 2000.
• [2] T. Salat, B.C. Tripathy, M. Zman, On some properties of I-convergence, Tatra Mt. Math. Publ. 28, (2004), 279-286.
• [3] E. E. Kara, M. Ilkhan, On some paranormed A-ideal convergent sequence spaces dened by Orlicz function, Asian Journal of Mathematics and Computer Research, 4(4), (2015), 183-194.
• [4] J. Lindenstrauss, L. Tzafriri, On Orlicz sequence spaces, Israel J. Math., Vol:10 No.3, (1971), 379-390.
• [5] S. D. Parashar, B. Choudhary, Sequence spaces dened by Orlicz function, Indian J. Pure Appl. Math., Vol:25, No.4, (1994), 419-428.
• [6] V. K. Bhardwaj, N. Singh, On some new spaces of lacunary strongly -sequences dened by Orlicz functions, Indian J. Pure Appl. Math., Vol:31, No.11, (2000), 1515-1526.
• [7] M. A. Krasnoselskii, Y. B. Rutitsky, Convex functions and Orlicz spaces, P. Noordhoff, Groningen, The Netherlands, 1961.
• [8] L. Maligranda, Orlicz spaces and interpolation, vol. 5 of Seminars in Mathematics, Polish Academy of Science, 1989.
• [9] J. Musielak, Orlicz spaces and Modular spaces, vol. 1043 of Lecture Notes in Mathematics, Springer, 1983.
• [10] H. Nakano, Modulared sequence spaces, Proc. Japan Acad. Ser. A Math. Sci., 27, (1951), 508-512.
• [11] S. Simons, The sequence spaces l (pv) and m(pv), Proc. London Math. Soc., 15, (1965), 422-436.
• [12] P. K. Kamptan, M. Gupta, Sequence spaces and series, Marcel Dekker, New York, 1980.
• [13] K. Raj, S.K. Sharma, Ideal convergent sequence spaces dened by a Musielak-Orlicz Function, Thai J. Math., 3, (2013), 577-587.
• [14] B.C: Tripathy, B. Hazarika, Some I-convergent sequence spaces dened by Orlicz Functions, Acta Math. Appl. Sin. Eng. Ser., 1, (2011), 149-154.
• [15] B. Hazarika, K. Tamang, B.K. Singh, On paranormed Zweier ideal convergent sequence spaces dened by Orlicz function, J. Egyptian Math. Soc., 22, (2014), 413-419.
• [16] M. Mursaleen, S.K. Sharma, Spaces of ideal convergent sequences, Hindawi Publishing Corporatiom The Scientic World Journal, 134534, (2014), 6 pages.
• [17] F. Bas.ar, Summability Theory and its Applications, Bentham Science Publishers, e-books, Monograph, _Istanbul, 2012.
• [18] H. Dutta, F. Bas.ar, A generalization of Orlicz sequence spaces by Cesaro mean of order one, Acta Math. Univ. Comen., 80(2), (2011), 185-200.
• [19] M. Bas.arir, S. Altundag, On generalized paranormed statistically convergent sequence spaces dened by Orlicz Function, Journal of Inequalities and Applications, Vol: 2009, 13 pages.