Results 11 to 20 of about 8,078 (282)
Orlicz–Pettis Theorem through Summability Methods
Mathematics, 2019 This paper unifies several versions of the Orlicz−Pettis theorem that incorporate summability methods. We show that a series is unconditionally convergent if and only if the series is weakly subseries convergent with respect to a regular linear ...
Fernando León-Saavedra +2 more
doaj +3 more sources
Dera Natung Government College Research Journal, 2023 We define the concept of rough limit set of a triple sequence space of beta Stancu operators of Borel summability of gradual real numbers and obtain the relation between the set of rough limit and the extreme limit points of a triple sequence space of ...
Arulmani İndumathi +2 more
doaj +1 more source
Rainwater-Simons-type convergence theorems for generalized convergence methods [PDF]
, 2010 We extend the well-known Rainwater-Simons convergence theorem to various generalized convergence methods such as strong matrix summability, statistical convergence and almost convergence.
Hardtke, Jan-David
core +4 more sources
Hausdorff summability methods, addendum [PDF]
Transactions of the American Mathematical Society, 1963 Three theorems are proven: (1) H st run. Concent alpha /sub 2/ (t,r)n.t.s. H st run. Concent alpha /sub 3/(t, r). (2) For b - 1> -k/log r, H st run. Concent alpha /sub 1/(t,k,b)n.t.s. H st run. Concent alpha / sub 3/(t,r) (3) For k> 4, H st run. Concent alpha /sub 1/(t,k + 1,c)n.t.s. H st run. Concent alpha /sub 1/(t,k,c).
openaire +2 more sources
An Analogue for Strong Summability of Abel's Summability Method [PDF]
Proceedings of the Edinburgh Mathematical Society, 1953 Given a series Σan, we define , by the relationwhere is the binomial coefficient . Let . If , the series Σan is said to be summable (C; k) to the sum s. If k > 0, p ≥ 1 and if, as n → ∞,we say that the series Σan is summable [C; k, p] to the sum s, or that the series is strongly summable (C; k) with index p to the sum s. If denotes the difference ,
Harington, C. F., Hyslop, J. M.
openaire +1 more source
A new factor theorem for generalized absolute Riesz summability
Karpatsʹkì Matematičnì Publìkacìï, 2019 The aim of this paper is to consider an absolute summability method and generalize a theorem concerning $\left|\bar{N},p_{n}\right|_{k}$ summability of infinite series to ${\varphi-\mid{\bar{N},p_n;\delta}\mid}_k$ summability of infinite series by using ...
A. Karakaş
doaj +1 more source
Ideal-quasi-Cauchy sequences [PDF]
, 2012 An ideal $I$ is a family of subsets of positive integers $\textbf{N}$ which is closed under taking finite unions and subsets of its elements.
Cakalli, Huseyin, Hazarika, Bipan
core +2 more sources
Relations on some Summability Methods [PDF]
Proceedings of the American Mathematical Society, 1993 In this paper we prove a new result connecting the summability methods | N ¯ , p n | k |\overline N ,{p_n}{|_k} with either
openaire +4 more sources
On Some New Ideal Convergent Sequence Spaces of -Method of Summability
Cumhuriyet Science Journal, 2017 In thepresent work, we introduce some ideal convergent sequence spaces by using - summability method which is defined by P. N. Natarajan [Onthe -method of summability, Analysis] as a typicallygeneralization of Nörlund method.
Şükran Konca, Nazlım Deniz Aral
doaj +1 more source
Summability Factors for Cesaro Methods [PDF]
Proceedings of the American Mathematical Society, 1979 It is shown that if each of r and s is a nonnegative integer and { f p } \{ {f_p}\} is a complex sequence such that Σ f p a p \Sigma {f_p}
openaire +1 more source