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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
https://izlik.org/JA69YH48LJ

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
https://izlik.org/JA69YH48LJ

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 Research Article
Authors

SELMA Altundag

MERVE Abay

Submission Date July 9, 2015
Publication Date October 1, 2016
IZ https://izlik.org/JA69YH48LJ
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. https://izlik.org/JA69YH48LJ
AMA 1.Altundag S, Abay M. SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION. Konuralp J. Math. 2016;4(2):169-176. https://izlik.org/JA69YH48LJ
Chicago Altundag, SELMA, and MERVE Abay. 2016. “SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION”. Konuralp Journal of Mathematics 4 (2): 169-76. https://izlik.org/JA69YH48LJ.
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 [1]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, Oct. 2016, [Online]. Available: https://izlik.org/JA69YH48LJ
ISNAD Altundag, SELMA - Abay, MERVE. “SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION”. Konuralp Journal of Mathematics 4/2 (October 1, 2016): 169-176. https://izlik.org/JA69YH48LJ.
JAMA 1.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, Oct. 2016, pp. 169-76, https://izlik.org/JA69YH48LJ.
Vancouver 1.SELMA Altundag, MERVE Abay. SOME SPACES OF A-IDEAL CONVERGENT SEQUENCES DEFINED BY MUSIELAK-ORLICZ FUNCTION. Konuralp J. Math. [Internet]. 2016 Oct. 1;4(2):169-76. Available from: https://izlik.org/JA69YH48LJ
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