Summability Factors Of Infinite Series Research Articles

On generalization of some theorems with absolute summability factors of infinite series

On generalization of some theorems with absolute summability factors of infinite series

On Absolute Matrix Summability of Factored Infinite Series and Fourier Series

– In this paper, we have generalized two known theorems dealing with the absolute weighted arithmetic mean summability factors of infinite series and Fourier series to the absolute matrix summability methods. Some new and known results have also been obtained.

On the summability factors of infinite series

On the summability factors of infinite series

Erratum to the paper: S. M. Mazhar, "On the summability factors of infinite series", Publ. Math. Debrecen, 13 (1966), 229-236

Erratum to the paper: S. M. Mazhar, "On the summability factors of infinite series", Publ. Math. Debrecen, 13 (1966), 229-236

On absolute weighted arithmetic mean summability of infinite series and Fourier series

Quite recently, we have obtained two main theorems dealing with absolute weighted arithmetic mean summability factors of infinite series and trigonometric Fourier series [C. R. Math. Acad. Sci. Paris 359 (2021), pp. 323–328]. In this paper, we have generalized these theorems for a general summability method. We have also obtained some new and known results for certain absolute summability methods.

Absolute weighted arithmetic mean summability of factored infinite series and Fourier series

In [Anal. Math. Phys., 8 (2018), 77-83], we have obtained two main theorems dealing with the |N¯,pn|k summability factors of infinite series and trigonometric Fourier series. In this paper, we have generalized these theorems for the |N¯,pn;θn|k summability methods. We have also obtained some new and known results for certain absolute summability methods.

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.

A NEW STUDY ON ABSOLUTE CESÀRO SUMMABILITY FACTORS

In this paper, we have generalized a known theorem dealing with $\varphi-{\mid{C},\alpha,\mid}_k$ summability factors of infinite series to the $\varphi-{\mid{C},\alpha,\beta\mid}_k$ summability method under weaker conditions. Also, some new and known results are obtained.

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.

Matrix Application of Power Increasing Sequences to Infinite Series and Fourier Series

UDC 517.54 The aim of the paper is a generalization, under weaker conditions, of the main theorem on quasi-$\sigma$-power increasing sequences applied to $|A,\theta_{n}|_{k}$ summability factors of infinite series and Fourier series. We obtain some new and known results related to basic summability methods.

A new factor theorem on generalized absolute Cesàro summability

In this paper, we have proved a general theorem dealing with the ϕ −| C, α, β |k summability factors of infinite series. Also, some new and known results are deduced.

On Generalized Absolute Matrix Summability of Infinite Series

In this paper, we have generalized a known theorem on \(|\bar{N},p_n|_{k}\) summability factors of infinite series with a new summability method by using almost increasing sequences. This new theorem also includes several new and known results.

A new study on generalized absolute Cesàro summability methods

In this paper, we have proved a known theorem dealing with ϕ — |C, α|k summability factors of infinite series under more weaker conditions. Also, some new results are obtained.

Absolute matrix summability via almost increasing sequence

In the present paper, a new theorem concerning absolute matrix summability factors, which generalizes a theorem on the summability factors of infinite series, has been proved by using almost increasing sequence and matrix transformation.

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.

A new result for weighted arithmetic mean summability factors of infinite series involving almost increasing sequences

In this paper, a known theorem dealing with weighted mean summability methods of non-decreasing sequences has been generalized for |A,p_{n};δ|_{k} summability factors of almost increasing sequences. Also, some new results have been obtained concerning |N,p_{n}|_{k}, |N,p_{n};δ|_{k} and |C,1;δ|_{k} summability factors.

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.

On Absolute Summability of Factored Infinite Series and Trigonometric Fourier Series

In this paper, a known result dealing with \(|\bar{N},p_{n};\theta _{n}|_{k}\) summability factors of infinite series, has been proved under weaker conditions. And then this result has been applied to the trigonometric Fourier series. Some new results have also been obtained.

A matrix application on absolute weighted arithmetic mean summability factors of infinite series

In this present paper, we have generalized a main theorem dealing with $|\bar{N}, p_{n}|_{k}$ summability of non-decreasing sequences to $|A, p_{n}|_{k}$ summability method by using almost increasing sequences and taking normal matrices in place of weighted mean matrices.