On I-convergent sequence spaces defined by a compact operator and a modulus function

References

• Basar, F., & Altay, B. (2003). On the spaces of sequences of p-bounded variation and related matrix mapping. Ukrainian Mathematical Journal, 55, 136–147.
   Google Scholar
• Bhardwaj, V. K. (2003). A generalization of a sequence space of Ruckle. Bulletin of Calcutta Mathematical Society, 95, 411–420.
   Google Scholar
• Buck, R. C. (1953). Generalized asymptotic density. American Journal of Mathematics, 75, 335–346.
   Web of Science ®Google Scholar
• Fast, H. (1951). Sur la convergence statistique [About statistical convergence]. Colloquium Mathematicum, 2, 241–244.
   Google Scholar
• Fridy, J. A. (1985). On statistical convergence. Analysis, 5, 301–313.
   Google Scholar
• Garling, D. J. H. (1966). On symmetric sequence spaces. Proceedings of the London Mathematical Society, 16, 85–106.
   Web of Science ®Google Scholar
• Gramsch, B. (1967). Die Klasse metrisher linearer Raume L(φ) [The class of metric linear spaces L(φ)]. Mathematische Annalen, 171, 61–78.
   Web of Science ®Google Scholar
• Khan, V. A. (2005). On a sequence space defined by modulus function. Southeast Asian Bulletin of Mathematics, 29, 1–7.
   Google Scholar
• Khan, V. A. (2006). Difference sequence spaces defined by a sequence modulii. Southeast Asian Bulletin of Mathematics, 30, 1061–1067.
   Google Scholar
• Khan, V. A. (2007). Statistically pre-Cauchy sequences and Orlicz function. Southeast Asian Bulletin of Mathematics, 6, 1107–1112.
   Google Scholar
• Khan, V. A., & Ebadullah, K. (2011). On some I-convergent sequence spaces defined by a modullus function. Theory and Applications of Mathematics and Computer Science, 1, 22–30.
   Google Scholar
• Khan, V. A., Ebadullah, K., Esi, A., & Shafiq, M. (2013). On some Zweier I-convergent sequence spaces defined by a modulus function. Africa Mathematika, Journal of the African Mathematical Society (Springer Verlag Berlin Heidelberg), 26, 115–125.
   Google Scholar
• Khan, V. A., Shafiq, M., & Rababah, R. K. A. (2015). On BVs I-convergent sequence spaces defined by an Orlicz function. Theory and Applications of Mathematics and Computer Science, 5, 62–70.
   Google Scholar
• Khan, V. A., & Tabassum, S. (2012). Statistically pre-Cauchy double sequences. Southeast Asian Bulletin of Mathematics, 36, 249–254.
   Google Scholar
• Kostyrko, P., Šalát, T., & Wilczyński, W. (2000). I-convergence. Raal Analysis Analysis Exchange, 26, 669–686.
   Google Scholar
• Köthe, G. (1970). Topological vector spaces (Vol. 1). Berlin: Springer.
   Google Scholar
• Kreyszig, E. (1978). Introductory functional analysis with applications. New York, NY: Wiley.
   Google Scholar
• Maddox, I. J. (1969). Some properties of paranormed sequence spaces. Journal of the London Mathematical Society, 1, 316–322.
   Google Scholar
• Maddox, I. J. (1986). Sequence spaces defined by a modulus. Mathematical Proceedings of the Cambridge Philosophical Society, 100, 161–166.
   Web of Science ®Google Scholar
• Nakano, H. (1953). Concave modulars. Journal of the Mathematical Society of Japan, 5, 29–49.
   Google Scholar
• Ruckle, W. H. (1967). Symmetric coordinate spaces and symmetric bases. Canadian Journal of Mathematics, 19, 828–838.
   Web of Science ®Google Scholar
• Ruckle, W. H. (1968). On perfect symmetric BK-spaces. Mathematische Annalen, 175, 121–126.
   Web of Science ®Google Scholar
• Ruckle, W. H. (1973). FK-spaces in which the sequence of coordinate vectors is bounded. Canadian Journal of Mathematics, 25, 973–975.
   Web of Science ®Google Scholar
• Šalát, T. (1980). On statistical convergent sequences of real numbers. Mathematica Slovaca, 30, 139–150.
   Google Scholar
• Šalát, T., Tripathy, B. C., & Ziman, M. (2004). On some properties of I-convergence. Tatra Mountains Mathematical Publications, 28, 279–286.
   Google Scholar
• Šalát, T., Tripathy, B. C., & Ziman, M. (2005). On I-convergence field. Italian Journal of Pure and Applied Mathematics, 17, 45–54.
   Google Scholar
• Schoenberg, I. J. (1959). The integrability of certain functions and related summability methods. American Mathematical Monthly, 66, 361–375.
   Google Scholar
• Sengönül, M. (2009). The Zweier sequence space. Demonstratio Mathematica, XL, 181–196.
   Google Scholar
• Tripathy, B. C. (1998). On statistical convergence. Proceedings of the Estonian Academy of Sciences. Physics. Mathematics Analysis, 47, 299–303.
   Google Scholar
• Tripathy, B. C., & Hazarika, B. (2009). Paranorm I-convergent sequence spaces. Mathematica Slovaca, 59, 485–494.
   Web of Science ®Google Scholar
• Tripathy, B. C., & Hazarika, B. (2011). Some I-convergent sequence spaces defined by Orlicz function. Acta Mathematicae Applicatae Sinica, 27, 149–154.
   Web of Science ®Google Scholar