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.     

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.     

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．     

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.     

An integral Riemann-Roch theorem for surface bundles

This paper is a response to a conjecture by T. Akita about an integral Riemann-Roch theorem for surface bundles.     

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.     

A general theorem characterizing some absolute summability methods

A general theorem is given which gives the necessary and sufficient conditions satisfied by a sequence (ε_n) in order to have the series Σa _n ε _n summable to |A| whenever Σa _n is summable to |A| for some summability methodA.     

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.     

An alternative method to obtain integral kernels for Lamé integral equations

In the present paper we introduce an alternative approach to obtain kernels for Lamé integral equations. The introduced procedure, based solely on simple algebraic manipulations, furnishes the well known kernels of hypergeometric form in an almost trivial manner without the use of transformations. More important, it provides a set of novel nuclei for Lamé integral equations in the form of Heun functions.     

An integral recursive inequality and applications

An integral recursive inequality for two functions is obtained. It is used to describe the equality cases in the related inequalities. The applications involve some bi-Hermitian forms, integral transformations, and confluent hypergeometric functions.      

An extension of the q-beta integral with applications

In this paper, we give an extension of the q-beta integral. Applications of the extension are also given, which include to derive an extension of the q-Pfaff-Saalschütz formula, an extension of the Kalnins and Miller transformations and a new identity for .     

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.     

Smoothed integral equations

For a linear integral equation there is a resolvent equation and a variation of parameters formula . It is assumed that B is a perturbed convex function and that a(t) may be badly behaved in several ways. When the first two equations are treated separately by means of a Liapunov functional, restrictive conditions are required separately on a(t) and B(t,s). Here, we treat them as a single equation where S is an integral combination of a(t) and B(t,s). There are two distinct advantages. First, possibly bad behavior of a(t) is smoothed. Next, properties of S needed in the Liapunov functional can be obtained from an array of properties of a(t) and B(t,s) yielding considerable flexibility not seen in standard treatment. The results are used to treat nonlinear perturbation problems. Moreover, the function is shown to converge pointwise and in L²[0,∞) to x(t).     

On the local properties of factored Fourier series

Quite recently, Bor [H. Bor, On the local properties of factored of Fourier series, Bull. Math. Anal. Appl. 1 (2009) 15-21] proved a theorem on the local property of summability of factored Fourier series. The purpose of this paper is to extend to more general cases by taking normal matrices in place of weighted mean matrices.     

Application of Almost Increasing Sequence for Absolute Riesz $|overline{N}, p_n^{alpha, beta}; delta|_k$ Summable Factor

In this paper, we generate an extended result by Bor and Seyhan concerning absolute Riesz summability factors. Further, we develop some well-known results from our main result.     

Extension of vector-valued integral polynomials

We study the extendibility of integral vector-valued polynomials on Banach spaces. We prove that an X-valued Pietsch-integral polynomial on E extends to an X-valued Pietsch-integral polynomial on any space F containing E, with the same integral norm. This is not the case for Grothendieck-integral polynomials: they do not always extend to X-valued Grothendieck-integral polynomials. However, they are extendible to X-valued polynomials. The Aron-Berner extension of an integral polynomial is also studied. A canonical integral representation is given for domains not containing ?₁.     

关于Tchebycheff—Fourier级数的（H,λ）平均的逼近

我们定义了（Ｈ，λ）求和法，它含有（Ｎ，ｐｎ），（Ｒ＾ｒｎ）和（Ｖｍｎ）求和法。讨论了函数ｆ（ｘ）∈Ｃ＾ｒ［－１，１］（ｒ∈Ｎ０）以及ｆ（ｘ）∈Ｗ＾ｒＨ＾ａ（ｒ∈Ｎ０，０＜ａ＜１）的切比晓夫－富里埃级数的逼近阶。