A new factor theorem for absolute Cesàro summability (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.

Summability factor relations between absolute weighted and Cesàro means

Mathematical Methods in the Applied Sciences, 2018

By , we denote the set of all sequences such that Σϵnan is summable V whenever Σan is summable U, where U and V are two summability methods. Recently, Sarıgöl has characterized the set for k > 1,α > −1 and arbitrary positive sequences Now, in the present paper, we characterize the sets , k > 1 and , k ≥ 1 for arbitrary positive sequences Hence we extend these results to the range α≥ − 1. In this way, some open problems in this topic are also completed.

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.

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.

Some Remarks on Summability Factors

Proceedings of The American Mathematical Society, 1976

showed that a necessary and sufficient condition for 2*°= i xk.yk t0 «>e Cesàro summable of order n (n is a nonnegative integer) whenever ak(y) = 0(k) where ak(y) is the k th Cesàro mean of y of order n is that 2f-i kn+l\An+1xk\ < oo and lim* ^/ex* = 0. The main result of Received by the editors October 8, 1974. AMS (MOS) subject classifications (1970). Primary 40D1S.

Some further extensions of absolute Cesàro summability for double series

Journal of Inequalities and Applications, 2013

In a recent paper [Savaş and Rhoades in Appl. Math. Lett. 22:1462-1466], the authors extended the result of Flett [Proc. Lond. Math. Soc. 7:113-141, 1957] to double summability. In this paper, we consider some further extensions of absolute Cesàro summability for double series. MSC: 40F05; 40G05