Convergent sequence spaces defined by positive function
*Maysoon A. NeamahCorresponding authormaysoon.azeez@ec.edu.iqDepartment of MathematicsFaculty of Open EducationGeneral Directorate of Education NajafNajaf, Iraqhttps://orcid.org/0000-0002-9691-3001View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Nov 2025
- Published Online:
- 27 Jun 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2556
- Pages:
- 1597–1606
Abstract
Keywords
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References
[1] J. Lindenstrauss, “Some aspects of the theory of Banach spaces,” Advances in Mathematics, vol. 5, no. 2, pp. 159–180 (1970).
[2] J. Lindenstrauss and L. Tzafriri, “On Orlicz sequence spaces,” Israel Journal of Mathematics, vol. 10, no. 3, pp. 379–390 (1971).
[3] M. Basarir and O. Solancan, “On some double sequence spaces,” Journal of the Indian Academy of Mathematics, vol. 21, no. 2, pp. 193–200 (1999).
[4] B. C. Tripathy and S. Borgohain, “Statistically convergent difference sequence spaces of fuzzy real numbers defined by Orlicz function,” Thai Journal of Mathematics, vol. 11, no. 2, pp. 357–370 (2013).
[5] B. C. Tripathy, “Generalized difference paranormed statistically convergent sequences defined by Orlicz function in a locally convex space,” Soochow Journal of Mathematics, vol. 30, no. 4, pp. 431–446 (2004).
[6] B. C. Tripathy and B. Sarma, “Vector valued double sequence spaces defined by Orlicz function,” Mathematica Slovaca, vol. 59, no. 6, pp. 767–776 (2009).
[7] T. J. I. A. Bromwich, An introduction to the theory of infinite series, vol. 335, Providence, RI, USA: American Mathematical Society (AMS Chelsea Publishing), pp. 535 (2005).
[8] V. D. Milman, “Geometric theory of Banach spaces. Part I. The theory of basis and minimal systems,” Russian Mathematical Surveys, vol. 25, no. 3, pp. 111–170 (1970), doi: 10.1070/RM1970v025n03ABEH003790.
[9] B. C. Tripathy and S. Mahanta, “On a class of generalized lacunary difference sequence spaces defined by Orlicz functions,” Acta Mathematicae Applicatae Sinica, English Series, vol. 20, no. 2, pp. 231–238 (2004).
[10] I. J. Schoenberg, “The integrability of certain functions and related summability methods,” The American Mathematical Monthly, vol. 66, no. 5, pp. 361–775 (1959).
[11] A. Zygmund, Trigonometric Series, 3rd ed., Cambridge: Cambridge University Press, pp. 784 (2003).
[12] T. Šalát, “On statistically convergent sequences of real numbers,” Mathematica Slovaca, vol. 30, no. 2, pp. 139–150 (1980).
[13] H. Fast, “Sur la convergence statistique,” in Colloquium Mathematicum, vol. 2, no. 3–4, pp. 241–244 (1951).
[14] J. Fridy and C. Orhan, “Statistical limit superior and limit inferior,” Proceedings of the American Mathematical Society, vol. 125, no. 12, pp. 3625–3631 (1997).
[15] I. J. Maddox, “A Tauberian theorem for statistical convergence,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 106, no. 2, pp. 277–280 (1989), doi: 10.1017/S0305004100078105.
[16] B. C. Tripathy, “On statistical convergence,” Proceedings of the Estonian Academy of Sciences, Physics and Mathematics, vol. 47, no. 4, pp. 299–303 (1998), doi: 10.3176/phys.math.1998.4.06.
[17] G. H. Hardy, “On the convergence of certain multiple series,” Proceedings of the London Mathematical Society, vol. 2, no. 1, pp. 124–128 (1904).
[18] B. C. Tripathy, “Statistically convergent double sequences,” Tamkang Journal of Mathematics, vol. 34, no. 3, pp. 231–237 (2003).
[19] F. Moricz, “Extensions of the spaces c and c0 from single to double sequences,” Acta Mathematica Hungarica, vol. 57, no. 1, pp. 129–136 (1991).
[20] D. Rath and B. C. Tripathy, “Matrix maps on sequence spaces associated with sets of integers,” Indian Journal of Pure and Applied Mathematics, vol. 27, pp. 197–206 (1996).
[21] K. Lindberg, “On subspaces of Orlicz sequence spaces,” Studia Mathematica, vol. 45, pp. 119–146 (1973).
[22] S. A. Al-Ameedee and A. J. Obaid, “New results and application of differential quasi subordinations for higher-order derivatives of meromorphic multivalent functions,” Journal of Interdisciplinary Mathematics, vol. 26, no. 4, pp. 643–650 (2023), doi: 10.47974/JIM-1483.
[23] F. Móricz and B. E. Rhoades, “Almost convergence of double sequences and strong regularity of summability matrices,” in Mathematical Proceedings of the Cambridge Philosophical Society, vol. 104, no. 2, pp. 283–294 (1988).
[24] A. Türkmenoğlu, “Matrix transformation between some classes of double sequences,” Journal of the Institute of Mathematics and Computer Sciences (Mathematical Series), vol. 12, no. 1, pp. 23–31 (1999).




