Generalised Riesz Typical Means

Definitions, notations and previous results. Let G{t) ≠ 0 be a continuous, positive, non-increasing function defined for t > 0 (if t < 0, set G{t) = 0), with G'(t)/G(t) non-decreasing and G(t) ∈ L(0, n) for every n > 0. Let λ = {λ_n} (n ≥ 0) be a strictly increasing unbounded sequence with λ₀ ≥ 0 and let s = {s_n} be an arbitrary sequence.