On absolute summability factors of infinite series

In this paper using δ-quasi-monotone sequences a theorem on summability factors of infinite series, which generalizes a theorem of Bor [4] on summability factors of infinite series, is proved. Also, in the special case this theorem includes a result of Mazhar [8] on |C, 1|_k summability factors.     

A note on two absolute summability methods

In this paper we have established a relation between |R,p _n ;δ|_k and |R,q _n ;δ|_k summability methods which generalizes the results of Bor [1] and Bosanquet [2].     

On the|\bar N,p_n | summability factors of infinite seriessummability factors of infinite series

In this paper a theorem of Chen [1] on summability factors of infinite series has been proved under weaker conditions.     

Generalized absolute Cesaro summability of a Fourier series

In an attempt to study the scope of a theorem due to Pati, the authors have established that φ(t) logK|t∈B _u V in (0,π)⟹ΣA _n (x) is |C, 0,β| forβ>1, at the pointt = x.     

Extension on absolute summability factors of infinite series

Extension and improvement has been made on a recent result proved by Mazhar [S.M. Mazhar, Absolute summability factors of infinite series, Kyungpook Math. J. 39 (1999) 67-73] concerning absolute summability factors of infinite series.     

A note on absolute summability factors

In this paper, by using an almost increasing and δ-quasi-monotone sequence, a general theorem on φ- | C, α | _k summability factors, which generalizes a result of Bor [3] on φ |C, 1| _k summability factors, has been proved under weaker and more general conditions.     

A note on absolute summability factors

Summary We obtain sufficient conditions for the series <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\sum a_{n}\lambda_{n}$ to be absolutely summable of order $k$ by a<span lang=FR style='font-size:10.0pt; mso-ansi-language:FR'>triangular matrix.     

General absolute summability factor theorems involving quasi-power-increasing sequences

In this paper a general theorem concerning the |A,δ|_k summability methods has been proved, which generalizes two results of Şevli and Leindler [H. Şevli and L. Leindler, On the absolute summability factors of infinite series involving quasi-power-increasing sequences, Computers and Mathematics with Applications 57 (2009), 702–709]. We obtain sufficient conditions for ∑a_nλ_n to be summable |A,δ|_k, k1, 0δ<1/k, by using quasi-power-increasing sequences.     

On general summability factor theorem of infinite series

A lower triangular matrix with nonzero principal diagonal entries is called a triangle. In this paper we obtain the sufficient conditions for ∑a_nλ_n to be summable ∣A∣_k whenever ∑a_n is summable ∣T∣_k for a triangle T.     

On a general theorem concerning some absolute summability methods

In this note a general theorem covering several absolute summability methods e.g, ¦N,p_n¦_k¦R,p_n¦_k, is proved.     

A note on absolute weighted mean summability factors

In this paper we have proved a main theorem concerning the | $\bar N$ , p _n; δ |_k summability methods, which generalizes a result of Bor and Özarslan [3].     

Multipliers for the absolute euler summability of fourier series

In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with miltipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.     

Application of the absolute Euler method to some series related to Fourier series and its conjugate series

We study the absolute Euler summability problem of some series associated with Fourier series and its conjugate series generalizing some known results in the literature. Also, it is shown that absolute Euler summability of rth derived Fourier series and rth derived conjugate series can be ensured under local conditions.     

On the absolute matrix summability of Fourier series and some associated series

The object of the paper is to study the absolute matrix summability problem of Fourier series, conjugate series and some associated series under a new set of conditions on matrix methods, generalising many known results in the literature.     

On application of matrix summability to Fourier series

Bor has recently obtained a main theorem dealing with absolute weighted mean summability of Fourier series. In this paper, we generalized that theorem for summability method. Also, some new and known results are obtained dealing with some basic summability methods.     

级数的常规可和，Cesàro可和与Abel可和的几点讨论

讨论级数常规可和、Cesaro可和与Abel可和的关系．利用数学分析级数理论,证明Abel可和适用范围最广,Cesaro可和其次,级数常规可和适用范围最小．这个结论丰富了经典级数理论,为实际应用中选用合适可和提供依据．     

Absolute matrix summability of the allied series of a Fourier series

In this paper we have proved a theorem for infinite triangular matrix using new techniques.     

Necessary and sufficient conditions for inclusion relations for absolute summability

We obtain a set of necessary and sufficient conditions for to imply for 1 <k ≤ s < ∞. Using this result we establish several inclusion theorems as well as conditions for the equivalence of and .     

On |A|k summability factors

Summary The paper deals with absolute summability factors for infinite series. The main result obtained in this paper generalizes a recent paper of Mazhar.     

Factors for ¦N,pn;δ¦k summability of Fourier series

In this paper two theorems on | N,p_n;δ|_k summability factors, which generalize the results of Bor [4] on | N,p_n|k summability factors, have been proved.