On \((N,p,q)\) summability factors of infinite series (Q1971656)

Recently Mishra, Sarigol, Bor and Sulaiman have obtained summability factor theorems for \(|N,p_n|_k\). In this paper the authors prove two theorems with necessary and sufficient conditions for \(\sum a_n\varepsilon_n\) to be summable \(|N,q|\) whenever \(\sum a_n\) is bounded \((N,p,q)\). Their theorems generalize and unify several known results of \textit{S. M. Mazhar} [Kodai Math. Semin. Rep. 18, 96-100 (1966), erratum ibid. 258 (1966; Zbl 0138.28301)] and \textit{E. C. Daniel} [J. Math. (Jabalpur) 2, 39-48 (1966)].