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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.1 Antofagasta Feb. 2020 


Some ideal convergent multiplier sequence spaces using de la Vallee Poussin mean and Zweier operator

Tanweer Jalal1 

1 National Institute of Technology, Dept. of Mathematics, Srinagar, JK, India. E-mail:


We introduce multiplier type ideal convergent sequence spaces, using Zweier transform and de la Vallee Poussin mean. We study some topological and algebraic properties of these spaces. Further we prove some inclusion relations related to these spaces.

Keywords: Ideal convergence; Zweier transform; Modulus function; De la Vallee Poussin mean

Texto completo disponible sólo en PDF.

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The author is thankful to the reviewers for their valuable suggestions and comments which improved the presentation of the paper.


[1] F. Başar and B. Altay, “On the spaces of sequences of p-bounded variation and related matrix mappings”, Ukrainian mathematical journal, vol. 55, pp. 136-147, Jan. 2003, doi: 10.1023/A:1025080820961. [ Links ]

[2] K. Demirci, “I-limit superior and limit inferior”, Mathematical communications, vol. 6, no. 2, pp. 165-172, 2001. [On line]. Available: ]

[3] D. J. H. Garling, “On symmetric sequence spaces”, Proceedings of the London mathematical society, vol. s3-16, no. 1, pp. 85-106, Jan. 1966, doi: 10.1112/plms/s3-16.1.85. [ Links ]

[4] D. J. H Garling, “Symmetric bases of locally convex spaces”, Studia mathematica, vol.30, pp. 163-181, 1968, doi: 10.4064/sm-30-2-163-181. [ Links ]

[5] B. Gramsch, “Die Klasse metrisher linearer Raume ℒφ”, Mathematische annalen, vol. 171, pp. 61-78, Mar. 1967, doi: 10.1007/BF01433094. [ Links ]

[6] T. Jalal , “Some new I-lacunary generalised difference sequence space in n-normed space”, in Modern mathematical methods and high performance computing in science and technology, vol. 171, V. Singh, H. Srivastava, E. Venturino, M. Resch, and V. Gupta , Eds. Singapore: Springer, 2016, pp. 249-258, doi: 10.1007/978-981-10-1454-3_21. [ Links ]

[7] T. Jalal, “On generalized A-difference strongly summable sequence space defined by ideal convergence on a real n-normed space”, Bulletin of the Calcutta mathematical society, vol. 106, no. 6, pp. 415-426, 2014. [ Links ]

[8] P. K. Kamthan and M. Gupta, Sequence spaces and series. New York, NY: Dekker, 1981. [ Links ]

[9] V. A. Khan, and K. Ebadullah, “On some I-convergent sequence spaces defined by a modulus function”, Theory and applications of mathematics & computer science, vol. 1, no. 2, pp. 22-30, Nov. 2011. [On line]. Available: ]

[10] V. A. Khan , K. Ebadullah, and Yasmeen, “On Zweier I-convergent sequence spaces”, Proyecciones (Antofagasta, On line), vol. 33, no. 3, pp. 259- 276, Sep. 2014, doi: 10.4067/S0716-09172014000300003. [ Links ]

[11] E. Kolk, “On strong boundedness and summability with respect to a sequence of modulii”, Acta et commentationes Universitatis Tartuensis, vol. 960, no. 1, pp. 41-50, 1993. [On line]. Available: ]

[12] E. Kolk, “Inclusion theorems for some sequence spaces defined by a sequence of moduli”, Acta et commentationes Universitatis Tartuensis , vol. 970, no. 1, pp. 65-72, 1994. [On line]. Available: ]

[13] P. Kostyrko, T. Sălát, and W. Wilczýnski, “I-convergence”, Real analysis exchange, vol. 26, no. 2, pp. 669-686, 2000. [On line]. Available: ]

[14] G. Köthe, Topological vector spaces I, Berlin: Springer, 1970. [ Links ]

[15] L. Leindler, “Über die de la Vallée-Poussinsche summierbarkeit allgenmeiner Orthogonalreihen”, Acta mathematica academiae scientiarum hungarica, vol. 16, no. 3-4, pp. 375- 387, Sep. 1965, doi: 10.1007/BF01904844. [ Links ]

[16] E. Malkowsky, “Recent results in the theory of matrix transformation in sequence spaces”, Matematički vesnik, vol. 49, no. 3-4, pp. 187-196, 1997. [On line]. Available: ]

[17] M. Et, P. Y. Lee and B. C. Tripathy, “Strongly almost (V,λ)(∆r)- summable sequences defined by Orlicz function”, Hokkaido mathematical journal, vol. 35, no. 1, pp. 197-213, Feb. 2006, doi:10.14492/hokmj/1285766306. [ Links ]

[18] M. Mursaleen and S. A. Mohiuddin, “On ideal convergence in probabilistic normed space”, Mathematica slovaca, vol. 62, no. 1, pp. 49-62, 2012, doi: 10.2478/s12175-011-0071-9. [ Links ]

[19] H. Nakano, “Concave modular”, Journal of the mathematical society of Japan, vol. 5, no. 1, pp. 29-49, 1953, doi:10.2969/jmsj/00510029. [ Links ]

[20] P. N. Ng, and P.Y. Lee, “Cesàro sequence spaces of non-absolute type”, Commentationes mathematicae, vol. 20, no. 2, pp. 429-433, 1978. [On line]. Available: Links ]

[21] W. H. Ruckle, “FK-spaces in which the sequence of coordinate vectors is bounded”, Canadian journal of mathematics, vol. 25, no. 5, pp. 973-975, Oct. 1973, doi: 10.4153/CJM-1973-102-9. [ Links ]

[22] W. H. Ruckle, “On perfect symmetric BK-spaces”, Mathematische annalen , vol. 175, no. 2, pp. 121-126, Jun. 1968, doi: 10.1007/BF01418767. [ Links ]

[23] W. H. Ruckle, “Symmetric coordinate spaces and symmetric bases”, Canadian journal of mathematics , vol. 19, pp. 828-838, 1967, doi: 10.4153/CJM-1967-077-9. [ Links ]

[24] T. Šalát, “On statistically convergent sequences of real numbers”, Mathematica slovaca , vol. 30, no. 2, pp. 139-150, 1980. [On line]. Available: ]

[25] T. Šalát, B. C. Tripathy, and M. Ziman, “On some properties of I-convergence”, Tatra mountains mathematical publications, vol. 28, pp. 279-286, 2004. [On line]. Available: Links ]

[26] T. Šalát , B. C. Tripathy and M. Ziman, “On I-convergence field”, Italian journal of pure and applied mathematics, vol. 17, pp. 45-54, 2005. [On line]. Available: Links ]

[27] M. Şengönül, “On the Zweier sequence space”, Demonstratio mathematica, vol.40, no. 1, pp. 181-196, 2007, doi: 10.1515/dema-2007-0119. [ Links ]

[28] B. C Tripathy and P. Chandra, “On some generalied difference paranormed sequence spaces associated with multiplier sequences defined by modulus functions”, Analysis in theory and applications, vol. 27, no. 1, pp. 21-27, Mar. 2011, doi: 10.1007/s10496-011-0021-y. [ Links ]

[29] B. C. Tripathy , and B. Hazarika, “Paranorm I-convergent sequence spaces”, Mathematica slovaca , vol. 59, no. 4, pp. 485-494, Jul. 2009, doi: 10.2478/s12175-009-0141-4. [ Links ]

[30] B. C. Tripathy and B. Hazarika, “I-convergent sequence spaces associated with multiplier sequence spaces”, Mathematical inequalities & applications, vol. 11, no. 3, pp. 543-548, 2008, doi: 10.7153/mia-11-43. [ Links ]

[31] B. C. Tripathy and S. Mahanta, “On a class of vector valued sequences associated with multiplier sequences”, Acta mathematicae applicatae sinica, vol. 20, no. 3, pp. 487-494, Sep. 2004, doi: 10.1007/s10255-004-0186-7. [ Links ]

[32] B. C. Tripathy and M. Sen, “On fuzzy I-convergent difference sequence spaces”, Journal of intelligent & fuzzy systems, vol. 25, no. 3, pp. 643-647, 2013, doi: 10.3233/IFS-120671. [ Links ]

[33] C. S. Wang, “On Nörlund sequence spaces”, Tamkang journal of mathematics, vol. 9, no. 2, pp. 269-274, 1978. [ Links ]

Received: June 2018; Accepted: August 2018

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