On some generalization of absolute Cesàro summability factors

On generalized absolute Cesàro summability

In this paper, a main theorem dealing with | C, 1 |k summability factors has been generalized under more weaker conditions for | C,α, β |k summability factors. This theorem also includes some new results. Mathematics Subject Classification 2000: 40D15, 40F05, 40G05, 40G99.

Factors for generalized absolute Cesàro summability

A positive sequence (bn) is said to be almost increasing if there exists a positive increasing sequence cn and two positive constants A and B such that Acn ≤ bn ≤ Bcn (see [1]). Obviously every increasing sequence is almost increasing but the converse need not be true as can be seen from the example bn = ne(−1) n . Let ∑ an be a given infinite series with partial sums (sn). We denote by tn n-th...

Generalization of Some Absolute Summability Methods

Mazhar (1971) gave the characterization for the series ∑ an n to be summable |N,pn|whenever ∑ an is summable |C,α|k, α≥ 0, k≥ 1. Here we prove two theorems, the first concerns the sufficient conditions and the second the necessary conditions satisfied by { n } in order to have ∑ an n summable |N̄,pn|k whenever ∑ an is summable |C,α|k, k≥ 1. 2000 Mathematics Subject Classification. Primary 40G. L...

Characterization on Some Absolute Summability Factors of Infinite Series

A general theorem concerning some absolute summability factors of infinite series is proved. This theorem characterizes as well as generalizes our previous result [4]. Other results are also deduced.

On absolute Nörlund summability factors