DOMAIN OF THE CESÀRO MEAN OF ORDER α IN MADDOX’S SPACE e(p)
Publications de l'Institut Mathematique, cilt.114, sa.128, ss.19-38, 2023 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 114 Sayı: 128
- Basım Tarihi: 2023
- Doi Numarası: 10.2298/pim2328019y
- Dergi Adı: Publications de l'Institut Mathematique
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
- Sayfa Sayıları: ss.19-38
- Anahtar Kelimeler: paranormed sequence space, alpha-, beta-and gamma-duals and matrix mappings
- Uşak Üniversitesi Adresli: Evet
Özet
The sequence space e(p) was defined by I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford (2), 18 (1967), 345— 355. Here, we introduce the paranormed Cesàro sequence space e(Cα, p) of order α, of non-absolute type as the domain of Cesàro mean Cα of order α and prove that the spaces e(Cα,.p) and e(p) are linearly paranorm isomorphic. Besides this, we compute the α-,β- and γ-duals of the space e(Cα,p) and construct the basis of the space e(Cα,p) together with the characterization of the classes of matrix transformations from the space e(Cα,p) into the spaces e∞ of bounded sequences and f of almost convergent sequences, and any given sequence space Y, and from a given sequence space Y into the sequence space e(Cα,p). Finally, we emphasize on some geometric properties of the space e(Cα,P).