Riesz I–convergent sequence spaces

• Khan, Vakeel A. ^[1] ; Rahman, Zahid ^[1]
  1. [1] Aligarh Muslim University

     Aligarh Muslim University

     India

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 6, 2023, págs. 1467-1487
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-5094
• Enlaces
  • Texto completo
• Resumen

  • In this article we have introduced some new sequence spaces  as a domain of triangular Riesz matrix, and study some of their algebraic and topological properties. Further, our work will devote to argue some inclosions regarding those fore-said sequence spaces.

• Referencias bibliográficas
  • M. Basarir, “On some new sequence spaces and related matrix transformations”, Indian J. Pure Appl. Math., vol. 26, pp. 1003-1010, 1995.
  • C. Aydin, and F. Basar, “Some generalizations of the sequence space arp”, Iran. J. Sci. Technol. Trans. A Sci., 2006.
  • M. Kirişçi, and F. Başar, “Some new sequence spaces derived by the domain of generalized difference matrix”, Comput. Math. Appl., vol. 60,...
  • M. Sengonül, and F. Başar, “Some new Cesaro sequence spaces of non-absolute type which include”, Soochow Journal of Mathematics, vol. 31,...
  • J. Boos, Classical and Modren Methods in Summability. Oxford University Press, Oxford, 2000
  • M. Sengonül, and K. Kayaduman, “On the Riesz Almost Convergent sequence spaces”, Abstr. Appl. Anal., vol. 2012, pp. 1-18, 2012.
  • E. Malkowsky, Mursaleen, and S. Suantai, “The dual spaces of sets of difference sequences of order m and matrix transformations”, Acta Math...
  • G. G. Lorentz, “A contribution to the theory of divergent sequences”, Acta Math., vol. 80, pp. 167-190, 1948.
  • J. Fridy, and C. Orhan, “Statistical limit superior and limit inferior”, Proc. Amer. Math. Soc., vol. 125, no. 12, pp. 3625-3631, 1997.
  • J. S. Connor, “The statistical and strong p-Cesaro convergence of sequences”, Analysis, vol. 8, no. 1-2, pp. 47-64, 1988.
  • O. Toeplitz, “Über allgemeine lineare Mittelbildungen”, Prace matematyczno-fizyczne, vol. 22, no. 1, pp. 113-119, 1911
  • G. M. Petersen, Regular matrix transformations. McGraw-Hill, 1966.
  • E. Malkowsky, and E. Savas, “Matrix transformations between sequence spaces of generalized weighted means”, Appl. Math. Comput., vol. 147,...
  • E. Malkowsky, and V. Rakočević, and S. Živković, “Matrix transformations between the sequence spaces w0p (Λ), v0p (Λ), c0p(Λ)(1¡ p¡) and certain...
  • G. C. Lascarides, and I. J. Maddox, “Matrix transformations between some classes of sequences”, Mathematical Proceedings of the Cambridge...
  • I. J. Maddox, “Spaces of strongly summable sequences”, The Quarterly Journal of Mathematics, vol. 18, no. 1, pp. 345-355, 1967.
  • I. J. Maddox, Elements of functional analysis, 1988.
  • E. Malkowsky, “Recent results in the theory of matrix transformations in sequence spaces”, Matematicki Vesnik-Beograd, vol. 49, pp. 187-196,...
  • S. Simons, “The sequence spaces l (pv) and m (pv)”, Proc. Lond. Math. Soc., vol. 1, no. 3, pp. 422-436, 1965.
  • A. Wilansky, Summability through functional analysis, pp. 1-318, 2000.
  • M. Başarır, and M. Öztürk, “On the Riesz difference sequence space”, Rend. Circ. Mat. Palermo, vol. 57, pp. 377-389, 2008.
  • V. A. Khan, “On Riesz-Musielak-Orlicz Sequence Spaces”, Numer. Funct. Anal. Optim., vol. 28, no. 7-8, pp. 883-895, 2007.
  • A. Balili, and A. Kiltho, “Some Generalized Difference Riesz Sequence Spaces and Related Matrix Transformations”, IOSR J. of Math., vol. 13,...
  • A. H. Ganie, and M. Ahmad, N. A. Sheikh, and, T. Jalal, “New type of Riesz sequence space of non-absolute type”, Int. J. Appl. Comput. Math.,...
  • H. Fast, “Sur la convergence statistique”, Colloquium mathematicae, vol. 2, pp. 241-244, 1951.
  • R. Filipów, and J. Tryba, “Ideal convergence versus matrix summability”, Studia Math., vol. 245, pp. 101-127, 2019.
  • V. A. Khan, and A. A. Sameera and K. M. A. S. Alshlool, and M. F. Khan, “Mohammad Faisal, On Zweier ideal convergence sequences in intuitionistic...
  • V. A. Khan, K. M. A. S. Alshlool, and A. A. Sameera “Spaces of ideal convergent sequences of bounded linear operators”, Numer. Funct. Anal....
  • V. A. Khan, K. M. A. S. Alshlool, S. A. A. Abdullah, R. K. A. Rababah, and A. Ahmad, “Some new classes of paranorm ideal convergent double...
  • V. A. Khan, and N. Khan, “On zweier I-convergent double sequence spaces”, Filomat, vol. 30, no. 12, pp. 3361-3369, 2016.
  • V. A. Khan, A. A. H. Makharesh, K. M. A. S. Alshlool, S. A. A. Abdullah, and H. Fatima, “On fuzzy valued lacunary ideal convergent sequence...
  • V. A. Khan, R. K. A. Rababah, K. M. A. S. Alshlool, S. A. A. Abdullah, and A. Ahmad, “On ideal convergence Fibonacci difference sequence spaces”,...
  • P. Kostyrko, M. Macaj, and T. Šalát, “Statistical convergence and I-convergence”, Real Anal. Exchange, vol. 25, no. 1, pp. 1-18, 1999.
  • T. Šalát, B. C. Tripathy, and M. Ziman, “On some properties of I-convergence”, Tatra Mt. Math. Publ, vol. 28, no. 2, pp. 274-286, 2004.
  • T. Šalát, B. C. Tripathy, and M. Ziman, “On I-convergence field”, Ital. J. Pure Appl. Math, vol. 17, no. 5, pp. 1-8, 2005.
  • H. Steinhaus, “Sur la convergence ordinaire et la convergence asymptotique”, Colloq. Math., vol. 2, pp. 73-74, 1951.
  • A. Wilansky, Summability through Functional Analysis. North-Holland, 1984.
  • V. A. Khan, K. M. A. S. Alshlool, and M. Alam, “On Hilbert I-convergent Sequence Spaces”, J. Math. Computer Sci., vol. 20, no. 3, pp. 225-233,...
  • M. Mursaleen and A. Latif, “Applications of measure of noncompactness in matrix operators on some sequence spaces”, Abstr. Appl. Anal., Hindawi,...
  • B. Altay, and F. Başar, F., “On the Paranormed Riesz Sequence Spaces of Non-absolute Type”, Southeast Asian Bull. Math., vol. 26, pp. 701-715,...
  • I. J. Maddox, “Paranormed sequence spaces generated by infinite matrices”, Mathematical Proceedings of the Cambridge Philosophical Society,...
  • B. C. Tripathy, and B. Hazarika, “I-convergent sequence spaces associated with multiplier sequences”, Mathematical Inequalities and Applications,...
  • B. C. Tripathy, and B. Hazarika, “Paranormed I-convergent Double Sequence Spaces Associated with Multiplier Sequences”, Kyungpook Math. J.,...
  • B. C. Tripathy, and M. Sen, “On fuzzy I-convergent difference sequence spaces”, Journal of Intelligent & Fuzzy Systems, vol. 25, no. 5,...
  • B. C. Tripathy, M. Sen, and S. Nath, “On Generalized Difference Ideal Convergence in Generalized Probabilistic n-normed Spaces”, vol. 91,...
  • B. C. Tripathy, M. Sen, and S. Nath, “I-convergence in probabilistic n-normed space”, Soft Comput, vol. 16, pp. 1021-1027, 2012. https://doi.org/10.1007/s00500-011-0799-8