Series summable (C, λ, μ) and applications

In this paper we deal with the convergence of the sequence in (x) = (x(1) + ... + x(n))/tau(n) for a given sequence tau = (tau(n))(n). Then we consider the (C, lambda, mu) summability that generalizes the (C, 1) summability and characterize the equivalence between the convergence of x(n)/tau(n) and the convergence of the sequence mu'(n) = 1/lambda(n) Sigma(n)(m=1), (mu) over cap (m) (x); and the equivalence between the convergence of in (tau) over cap (n) (x) and the convergence of mu'(n). (C) 2012 Published by Elsevier Inc.