Kushwaha Jitendra Kumar
Department of Pure & Applied Mathematics, Guru Ghasidas University, Koni, Bilaspur 495009, India.
ScientificWorldJournal. 2013 Nov 26;2013:508026. doi: 10.1155/2013/508026. eCollection 2013.
Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler's mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler's means of conjugate of functions belonging to Lip (ξ(t), p) class has been obtained. Lipα and Lip (α, p) classes are the particular cases of Lip (ξ(t), p) class. The main result of this paper generalizes some well-known results in this direction.
逼近论是一个非常重要的领域，在纯数学和应用数学中有各种应用。本研究涉及一个关于用傅里叶级数共轭级数的欧拉均值逼近李普希茨类函数的新定理。本文得到了属于Lip(ξ(t), p)类函数的共轭函数的欧拉均值的逼近度。Lipα和Lip(α, p)类是Lip(ξ(t), p)类的特殊情况。本文的主要结果推广了该方向上一些著名的结果。
