Multiplication of Strongly Summable Series

Abstract

Given a series we define , by the relationsThe series is said to be summable (C, k), where k > - 1, to the sum s ifto be summable (C, - 1) to s if it converges to s and nan = o(l); to be absolutely summable (C, k), or summable | C, k, to s if it is summable (C, k) to s andand to be strongly Cesàro summable to s with order k > 0 and index p or summable [C; k, p] to s, if