A remark on a theorem of A. B. Németh regarding the convergence of sequences of linear operators on space C[a,b]
For a sequence x ∈ ℓ₁∖c₀₀, one can consider the set E(x) of all subsums of the series . Guthrie and Nymann proved that E(x) is one of the following types of sets: () a finite union of closed intervals; () homeomorphic to the Cantor set; homeomorphic to the set T of subsums of where b(2n-1) = 3/4ⁿ and b(2n) = 2/4ⁿ. Denote by ℐ, and the sets of all sequences x ∈ ℓ₁∖c₀₀ such that E(x) has the property (ℐ), () and ( ), respectively. We show that ℐ and are strongly -algebrable and is -lineable. We...
Zeta-generalized-Euler-constant functions, and defined on the closed interval [0, ∞), where γ(1) is the Euler-Mascheroni constant and (1) = ln , are studied and estimated with high accuracy.