Nörlund Di¤erence Sequence spaces in 2-normed spaces using Orlicz function
Résumé
In this paper, we introduce the concept of paranormed Nörlund-difference sequence spaces with Orlicz function over 2-normed spaces denoted by N^{t}(Δ,M,p,‖.,.‖)_{c₀}, N^{t}(Δ,M,p,‖.,.‖)_{c} and N^{t}(Δ,M,p,‖.,.‖)_{ℓ_{∞}} with Δ-transform are in c₀,c and ℓ_{∞}. Additionally, we investigate various topological characteristics of these spaces and analyze various inclusion relationships between these spaces. Furthermore, we establish and construct the α-,β- and γ-duals of these spaces, along with establishing the Schauder basis for N^{t}(Δ,M,p,‖.,.‖)_{c₀} and N^{t}(Δ,M,p,‖.,.‖)_{c}.
Téléchargements
Références
[2] M. Et and R. Çolak; On some generalized di¤erence sequence spaces, Soochow J. Math., 21(4), 377386 (1995).
[3] W. R. Freese and J. Cho; Geometry of linear 2-normed spaces, Nova Science Publishers, Inc., Hauppauge, NY, (2001).
[4] S. Gähler; 2-metrische Räume und ihre topologische Struktur, Math.Nachr., 26, 115148 (1963).
[5] H. Gunawan and Mashadi; On nite-dimensional 2-normed spaces, Soochow J. Math., 27(3), 321329 (2001).
[6] K. G. Grosse-Erdmann; Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180(1), 223238 (1993).
[7] H. K¬zmaz; On certain sequence spaces, Canad. Math. Bull., 24(2), 169176(1981).
[8] G. C. Lascarides and I. J. Maddox; Matrix transformations between some classes of sequences, Proc. Cambridge Philos. Soc., 68, 99104 (1970).
[9] J. Lindenstrauss and L. Tzafriri; On Orlicz sequence spaces, Israel J. Math.,
10, 379-390 (1971).
[10] I. J. Maddox; Elements of functional analysis, Cambridge University Press,Cambridge, (1988).
[11] I. J. Maddox; Paranormed sequence spaces generated by infinite matrices, Proc. Cambridge Philos. Soc., 64, 335340 (1968).
[12] I. J. Maddox; Spaces of strongly summable sequences, Quart. J. Math. Oxford Ser. (2), 18, 345-355 (1967).
[13] E. Malkowsky and E. Savas; Matrix transformations between sequence spaces of generalized weighted means, Appl. Math. Comput., 147(2), 333
345 (2004).
[14] M. F. Mears; The inverse Nörlund mean, Ann. of Math., 44, 401-410 (1943).
[15] M. Mursaleen, Sunil K. Sharma and A. K¬l¬çman; Sequence spaces defined by Musielak-Orlicz function over n-normed spaces, Abstr. Appl. Anal., Art.ID 364743, pp. 10, (2013).
[16] M. Mursaleen; Generalized spaces of di¤erence sequences, J. Math. Anal. Appl., 203(3), 738-745 (1996).
[17] M. Mursaleen; On some new invariant matrix methods of summability, Quart. J. Math. Oxford Ser., 34(133), 77-86 (1983).
[18] H. Nakano; Modulared sequence spaces, Proc. Japan Acad., 27(2), 508-512(1951).
[19] A. Peyerimho¤; Lectures on summability, Lecture Notes in Mathematics, Vol. 107, (1969).
[20] K. Raj and S. K. Sharma; Some sequence spaces in 2-normed spaces defined by Musielak-Orlicz function, Acta Univ. Sapientiae Math., 3(1), 97-109
(2011).
[21] K. Raj, S. K. Sharma and A. K. Sharma; Difference sequence spaces in n-
normed spaces de ned by Musielak-Orlicz function, Armen. J. Math., 3(3), 127-141 (2010).
[22] K. Raj, A. K. Sharma and S. K. Sharma; A sequence space defined by Musielak-Orlicz function, Int. J. Pure Appl. Math., 67(4), 475-484 (2011).
[23] S. Simons; The sequence spaces l(p) and m(p), Proc. London Math. Soc., 15(3), 422-436 (1965).
[24] S. Singh and T. A. Malik; Paranormed Norlund Nt-difference sequence spaces and their ; and duals, Proyecciones, 42(4), 879-892 (2023).
[25] A. Wilansky; Summability through functional analysis, North-Holland Mathematics Studies, vol. 85, (1984).
[26] M. Ye¸silkayagil and F. Ba¸sar; On the paranormed Nörlund sequence space of nonabsolute type, Abstr. Appl. Anal., Art. ID 858704, pp. 9, (2014).
Copyright (c) 2026 Boletim da Sociedade Paranaense de Matemática
Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
