Application of Quasi ‘ f ’ power Increasing Sequences in Absolute Summability (original) (raw)

Application of quasi-f -power increasing sequence in absolute ph - |C, a, b; d; l| of infinite series

Mathematica Moravica

An increasing quasi-f-power sequence of a wider class has been used to establish a universal theorem on a least set of conditions, which is sufficient for an infinite series to be generalized ph-|C, a, b; d; l| k summable. Further, a set of new and well-known arbitrary results have been obtained by using the main theorem. Considering suitable conditions a previous result has been obtained, which validates the current findings. In this way, Bounded Input Bounded Output(BIBO) stability of impulse has been improved by finding a minimal set of sufficient condition for absolute summability because absolute summable is the necessary and sufficient conditions for BIBO stability.

Sufficient Conditions for Absolute Cesàro Summable Factor

International Journal of Mathematical, Engineering and Management Sciences

Quasi-f-power increasing sequence has been used for infinite series to establish a theorem on a minimal set of sufficient conditions for absolute Cesàro φ-|〖C,α;δ;l|〗_k summable factor. Further, a set of new and well-known arbitrary results have been obtained by using the main theorem. The presented main result has been validated by the previous result under suitable conditions. In this way, the Bounded Input Bounded Output (BIBO) stability of impulse response has been improved by finding a minimal set of sufficient conditions for absolute summability because absolute summable is the necessary and sufficient condition for BIBO stability.

Indexed Absolute Cesaro Summability for Infinite Series

The Nepali Mathematical Sciences Report

In the present study, a wider class of sequence is used for a least set of sufficient conditions for absolute Cesàro ϕ − |C, α, β; δ; γ| k summable factor for an infinite series. Many corollaries have been determined by using sutaible conditions in the main theorem. Validation of the theorem done by the previous findings of summablity. In this way, system's stability is improved by finding the conditions for absolute summability.

A New Result on Generalized Absolute Cesàro Summability

2016

In [4], a main theorem dealing with an application of almost increasing sequences, has been proved. In this paper, we have extended that theorem by using a general class of quasi power increasing sequences, which is a wider class of sequences, instead of an almost increasing sequence. This theorem also includes some new and known results.

Quasi-power increasing sequence for generalized absolute summability

Nonlinear Analysis: Theory, Methods & Applications, 2008

In this paper, we prove a theorem given in [E. Savaş, On almost increasing sequences for generalized absolute summability, Math. Inequal. Appl., Preprint] on summability factors under weaker conditions by using a quasi-β-power increasing sequence instead of an almost increasing sequence.

On the absolute summability factors of infinite series involving quasi-power-increasing sequences

Computers & Mathematics with Applications, 2009

In this paper, we prove two theorems on |A| k , k 1, summability factors for an infinite series by replacing a Riesz matrix with a lower triangular matrix and using quasipower-increasing sequences instead of almost increasing sequences. We obtain sufficient conditions for a n λ n to be summable |A| k , k 1, by using quasi-f -increasing sequences.

A theorem on the Cesàro summability method

Computers & Mathematics with Applications, 2011

In this paper we retrieve the backward Cesàro convergence of a real sequence u = (u n ) from the Cesàro summability of the general control modulo of the oscillatory behavior of integer order m of (u n ) under certain conditions.