On the generalized Cesàro sequence spaces and some of their properties
TURKISH JOURNAL OF MATHEMATICS, cilt.50, sa.5, ss.933-949, 2026 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 50 Sayı: 5
- Basım Tarihi: 2026
- Doi Numarası: 10.55730/1300-0098.3775
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM), Academic Search Ultimate (EBSCO)
- Sayfa Sayıları: ss.933-949
- İstanbul Kültür Üniversitesi Adresli: Evet
Özet
Let C-t = (c(nm))(n,m is an element of N) denote the generalized Cesaro matrix defined by c(nm) = t(n-m/)n for m <= n and t is an element of [0, 1], and c(nm) = 0 otherwise. For each q is an element of [1, co), the associated generalized Ces & agrave;ro sequence spaces cestq are introduced. These spaces form Banach lattices under the coordinatewise order, equipped with a naturally defined order continuous norm. We prove that ces(q)(t) = ces(q)(0) for all t E [0, 1) and q is an element of [1, co), implying that the space cestq is a weighted & ell;(q) space with equivalent norm. Furthermore, we examine the inclusion relationships between ces(q) and ces(q)(t) , and establish that cesq is a proper subspace of cestq whenever t is an element of [0, 1). Finally, we explore various geometric properties of these spaces, including the characterization of extreme points of the unit ball, strict convexity, (nearly) uniform convexity, (nearly) uniform smoothness, and property (beta).