Absolute φ − | C , α , β ; δ | k φ−∣C,α,β;δ∣k\varphi- \vert C, \alpha, \beta; \delta\vert _{k}φ−∣C,α,β;δ∣k​ summability of infinite series (original) (raw)

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.

Absolute summability factor \varphi-|C,1;\delta|_k of infinite series

International Journal of Mathematical Analysis, 2016

In this paper, we established a generalized theorem on absolute summability factors by applying a recently defined absolute Cesàro summability ϕ − |C, 1; δ| k and the concept of a quasi-f-power increasing sequence for infinite series. We further obtained a well-known result under suitable conditions.

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.

Application of Quasi ‘ f ’ power Increasing Sequences in Absolute Summability

Procedia Computer Science, 2018

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.

ON SOME PROPERTIES OF SUMMABILITY THEORY

By considering certain special sequences, we have determined convergence or divergence in the Cesaro sense for series constructed using specific sequences. This is done for family of series which depends on a particular parameter k. Moreover, these techniques are viewed as generalized version of standard Cesaro Summability methods.

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.