Absolute Riesz Summability Factors Research Articles

On absolute matrix summability factors of infinite series and Fourier series

Quite recently, Bor (2021) [22] has proved two main theorems dealing with absolute Riesz summability factors of infinite series and Fourier series by using an almost increasing sequence. In this paper, we have generalized these theorems to the |A,pn|k summability method.

A New Application of a Wider Class of Power Increasing Sequences

In the present paper, we have proved a basic theorem on the absolute Riesz summability factors of infinite series by using a wider class of power increasing sequences and then we applied this new result to the trigonometric Fourier series. Some new results are also obtained concerning the factored infinite series and trigonometric Fourier series.

ON A NEW APPLICATION OF QUASI POWER INCREASING SEQUENCES

In the present paper, absolute matrix summability of infinite series has been studied. A new theorem concerned with absolute matrix summability factors, which generalizes a known theorem dealing with absolute Riesz summability factors of infinite series, has been proved under weaker conditions by using quasi $\beta$-power increasing sequences. Also, a known result dealing with absolute Riesz summability has been given.

On a new application of quasi power increasing sequences

In the present paper, absolute matrix summability of infinite series has been studied. A new theorem concerned with absolute matrix summability factors, which generalizes a known theorem dealing with absolute Riesz summability factors of infinite series, has been proved under weaker conditions by using quasi $\beta$-power increasing sequences. Also, a known result dealing with absolute Riesz summability has been given.

Certain new factor theorems for infinite series and trigonometric fourier series

In this paper, firstly we proved a general theorem dealing with absolute Riesz summability factors of infinite series under weaker conditions. And secondly we applied it to the trigonometric Fourier series. Also we have obtained some new and known results.

A New Note on Absolute Weighted Arithmetic Mean Summability

We generalize a known result dealing with absolute Riesz summability factors of infinite series by using a wider class of power increasing sequences. Some new and known results are also obtained.

On absolute Riesz summability factors of infinite series and their application to Fourier series

Abstract In this paper, some known results on the absolute Riesz summability factors of infinite series and trigonometric Fourier series have been generalized for the | N ¯ , p n ; θ n | k {\lvert\bar{N},p_{n};\theta_{n}\rvert_{k}} summability method. Some new and known results are also obtained.

On some new results for non-decreasing sequences

In this paper, a general theorem on absolute Riesz summability factors of infinite series is proved under weaker conditions. Also we have obtained some new and known results.

On the generalization of a theorem of Bor

In [ Filomat, 28 (2014), 1537-1541], Bor proved a theorem dealing with absolute Riesz summability factors of infinite series. In this paper, we generalize that result for the absolute matrix summability factors of infinite series. Some new results are also obtained.

Some new results on absolute Riesz summability of infinite series and Fourier series

In this paper, some known results on the absolute Riesz summability factors of infinite series and Fourier series have been proved under weaker conditions. Some new and known results are also obtained.

A new theorem on the absolute Riesz summability factors

In [5], we proved a main theorem dealing with absolute Riesz summability factors of infinite series using a quasi-?-power increasing sequence. In this paper, we generalize that theorem by using a general class of power increasing sequences instead of a quasi-?-power increasing sequence. This theorem also includes some new and known results.

A study on absolute Riesz summability factors

In the present paper, two general theorems on\(|\bar N,p_n ;\delta |_k \) summability factors of infinite series which generalize some known results, have been proved. Also we have obtained two new results concerning the |C,1;δ|k summability factors.

A note on absolute Riesz summability factors

A note on absolute Riesz summability factors

On two absolute Riesz summability factors of infinite series

This paper gives a necessary and sufficient condition in order that a series ∑ a n ε n \sum {{a_n}} {\varepsilon _n} should be summable | R , q n | |R,{q_n}| whenever ∑ a n \sum {{a_n}} is summable | R , p n | k , k ⩾ 1 |R,{p_n}{|_k},\;k \geqslant 1 , and so extends the known result of Bosanquet to the case k > 1 k > 1 .

Absolute Riesz summability factors of Fourier series

Absolute Riesz summability factors of Fourier series

On absolute Riesz summability factors of Fourier series

On absolute Riesz summability factors of Fourier series

A theorem on the absolute Riesz summability factors of a Fourier series

A theorem on the absolute Riesz summability factors of a Fourier series

Absolute Riesz summability factors for Fourier series

Let ∑an be a given infinite series and {λn} a non-negative, strictly increasing, monotonic sequence, tending to infinity with n. We write, for w > λ0,and, for r>0, we write is known as the Riesz sum of “ type ” λn and “ order ” r, andis called the Riesz mean of type λn and order r.