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

Year 2016, Volume: 4 Issue: 2, 169 - 176, 01.10.2016

Abstract

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.

References

  • [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.
Year 2016, Volume: 4 Issue: 2, 169 - 176, 01.10.2016

Abstract

References

  • [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.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

SELMA Altundag

MERVE Abay

Publication Date October 1, 2016
Submission Date July 9, 2015
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Altundag, S., & Abay, M. (2016). SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION. Konuralp Journal of Mathematics, 4(2), 169-176.
AMA Altundag S, Abay M. SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION. Konuralp J. Math. October 2016;4(2):169-176.
Chicago Altundag, SELMA, and MERVE Abay. “SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION”. Konuralp Journal of Mathematics 4, no. 2 (October 2016): 169-76.
EndNote Altundag S, Abay M (October 1, 2016) SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION. Konuralp Journal of Mathematics 4 2 169–176.
IEEE S. Altundag and M. Abay, “SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION”, Konuralp J. Math., vol. 4, no. 2, pp. 169–176, 2016.
ISNAD Altundag, SELMA - Abay, MERVE. “SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION”. Konuralp Journal of Mathematics 4/2 (October 2016), 169-176.
JAMA Altundag S, Abay M. SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION. Konuralp J. Math. 2016;4:169–176.
MLA Altundag, SELMA and MERVE Abay. “SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION”. Konuralp Journal of Mathematics, vol. 4, no. 2, 2016, pp. 169-76.
Vancouver Altundag S, Abay M. SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION. Konuralp J. Math. 2016;4(2):169-76.
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