Warianty tytułu
Języki publikacji
Abstrakty
In this article, we introduce and study sequence spaces of Cesàro-Nörlund operators of order n associated with a sequence of Orlicz functions.We obtain some topological properties and Schauder basis of these sequence spaces.Moreover, we compute the α-, β- and γ-duals and the matrix transformations of these newly formed sequence spaces. Finally, we prove that these sequence spaces are of Banach-Saks type p and have a weak fixed-point property.
Czasopismo
Rocznik
Tom
Strony
229--238
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- School of Mathematics, Shri Mata Vaishno Devi University, Katra-182320, India, usinghiitg@gmail.com
autor
- School of Mathematics, Shri Mata Vaishno Devi University, Katra-182320, India, swatijasrotia12@gmail.com
autor
- School of Mathematics, Shri Mata Vaishno Devi University, Katra-182320, India, kuldipraj68@gmail.com
Bibliografia
- [1] F. Başar, Summability Theory and its Applications, Bentham Science, Oak Park, 2012.
- [2] B. Beauzamy, Banach-Saks properties and spreading models, Math. Scand. 44 (1979), no. 2, 357-384.
- [3] A. J. Dutta, A. Esi and B. C. Tripathy, Statistically convergent triple sequence spaces defined by Orlicz function, J. Math. Anal. 4 (2013), no. 2, 16-22.
- [4] J. García Falset, The fixed point property in Banach spaces with the NUS-property, J. Math. Anal. Appl. 215 (1997), no. 2, 532-542.
- [5] G. H. Hardy, An inequality for Hausdorff means, J. London Math. Soc. 18 (1943), 46-50.
- [6] G. H. Hardy, Divergent Series, Oxford University, Oxford, 1949.
- [7] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, 2nd ed., Cambridge University, Cambridge, 1952.
- [8] H. Knaust, Orlicz sequence spaces of Banach-Saks type, Arch. Math. (Basel) 59 (1992), no. 6, 562-565.
- [9] G. Köthe and O. Toeplitz, Lineare Räume mit unendlich vielen Koordinaten und Ringe unendlicher Matrizen, J. Reine Angew. Math. 171 (1934), 193-226.
- [10] J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 10 (1971), 379-390.
- [11] F. M. Mears, The inverse Nörlund mean, Ann. of Math. (2) 44 (1943), 401-410.
- [12] M. Mursaleen, Applied summability methods, Springer Briefs Math., Springer, Cham, 2014.
- [13] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, Berlin, 2006.
- [14] K. Raj and A. Kılıçman, On certain generalized paranormed spaces, J. Inequal. Appl. 2015 (2015), Paper No. 37.
- [15] H. Roopaei, D. Foroutannia, M. İlkhan and E. E. Kara, Cesàro spaces and norm of operators on these matrix domains, Mediterr. J. Math. 17 (2020), no. 4, Paper No. 121.
- [16] M. Stieglitz and H. Tietz, Matrixtransformationen von Folgenräumen. Eine Ergebnisübersicht, Math. Z. 154 (1977), no. 1, 1-16.
- [17] B. C. Tripathy, A. Esi and B. Tripathy, On a new type of generalized difference Cesàro sequence spaces, Soochow J. Math. 31 (2005), no. 3, 333-340.
- [18] C. S. Wang, On Nörlund sequence spaces, Tamkang J. Math. 9 (1978), no. 2, 269-274.
- [19] A. Wilansky, Summability Through Functional Analysis, North-Holland, Amsterdam, 1984.
- [20] M. Yeşilkayagil and F. Başar, On the paranormed Nörlund sequence space of nonabsolute type, Abstr. Appl. Anal. 2014 (2014), Article ID 858704.
- [21] M. Yeşilkayagil and F. Başar, Domain of the Nörlund matrix in some of Maddox’s spaces, Proc. Nat. Acad. Sci. India Sect. A 87 (2017), no. 3, 363-371.
- [22] M. Zeltser, M. Mursaleen and S. A. Mohiuddine, On almost conservative matrix methods for double sequence spaces, Publ. Math. Debrecen 75 (2009), no. 3-4, 387-399.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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