Application of Quasi 'f' power Increasing Sequences in Absolute Summability

A theorem has been developed to acquire a set of conditions which is sufficient for an infinite series to be a generalized Cesàro φ-|C, α; δ|k summable using a wider class of sequence. Further, a conventional result has also been deduced from the main results under suitable conditions, which is a validation of the present result by the previous result. Using quasi 'f ' power increasing sequence, the Bounded Input Bounded Output (BIBO) stability of impulse response has been improved for modelling an infinite series to be absolute summable by estimating sufficient conditions which are also necessary and sufficient conditions for an infinite series to be BIBO stable.