On Convergence and Summability with Speed II
Ants Aasma, Hemen Dutta, P.N. Natarajan · 2017
In this chapter, the authors focuses on the study of convergence, boundedness, and summability with speed. They assumes that λ = (λk) (called the speed of convergence or summability) is a sequence with 0 < λk ↗ ∞ if not specified otherwise. The notions of λ-reversible and λ-perfect matrix methods are introduced. The authors present some topological properties of the spaces mλ, cλ, cλ A, and mλ A. Necessary and sufficient conditions for M ε (cλ A,mμ B), M ε (cλ A, cμ B), and for the Mseq-consistency of A and B on cλ A (μ is another speed and B is another matrix method) are described. As an application of the main results, the matrix transforms for the cases of Riesz and Cesaro methods are investigated.