Nörlund Di¤erence Sequence spaces in 2-normed spaces using Orlicz function
Resumo
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}.
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Referências
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[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).
[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).
Publicado
2026-04-09
Seção
Special Issue: Advances in Mathematical Sciences
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