A Tauberian theorem for the generalized Nörlund summability method
Articles > Article · 2018
Authors: İbrahim ÇANAK, Naim L. Braha, Umit Totur
Georgian Mathematical Journal, Journal Indexed in SCI Expanded, International, WoS, 2018, vol 27, pp 31-36
Summary
Abstract Let ( p n ) {(p_{n})} and ( q n ) {(q_{n})} be any two non-negative real sequences, with R n := ∑ k = 0 n p k q n - k ≠ 0 {R_{n}:=\sum_{k=0}^{n}{p_{k}q_{n-k}}\neq 0} ( n ∈ ℕ {n\in\mathbb{N}} ). Let ∑ k = 0 ∞ a k {\sum_{k=0}^{\infty}a_{k}} be a series of real or complex numbers with partial sums ( s n ) {(s_{n})} , and set t n p , q := 1 R n ∑ k = 0 n p k q n - k s k {t_{n}^{p,q}:=\frac{