Trigonometric Approximation of Signals (Functions) Belonging to the <i>Lip</i>(<i>ξ</i>(<i>t</i>),<i>r</i>),(r>1)-Class by (<i>E</i>,<i>q</i>) (<i>q</i>>0)-Means of the Conjugate Series of Its Fourier Series

作     者：Vishnu Narayan Mishra Huzoor H. Khan Idrees A. Khan Kejal Khatri Lakshmi N. Mishra 

作者机构：Department of Applied Mathematics & Humanities Sardar Vallabhbhai National Institute of Technology Surat India Department of Mathematics Aligarh Muslim University Aligarh India Dr. Ram Manohar Lohia Avadh University Faizabad India 

出 版 物：《Advances in Pure Mathematics》 (理论数学进展（英文）)

年 卷 期：2013年第3卷第3期

页      面：353-358页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Signals Conjugate Fourier Series Trigonometric Fourier Approximation Degree of Approximation Lip(ξ(t) r)-Class (E q) Summability 

摘      要：Various investigators such as Khan ([1-4]), Khan and Ram [5], Chandra [6,7], Leindler [8], Mishra et al. [9], Mishra [10], Mittal et al. [11], Mittal, Rhoades and Mishra [12], Mittal and Mishra [13], Rhoades et al. [14] have determined the degree of approximation of 2π-periodic signals (functions) belonging to various classes Lipα, Lip(α,r), Lip(ξ(t),r) and W(Lr,ζ(t)) of functions through trigonometric Fourier approximation (TFA) using different summability matrices with monotone rows. Recently, Mittal et al. [15], Mishra and Mishra [16], Mishra [17] have obtained the degree of approximation of signals belonging to -class by general summability matrix, which generalizes the results of Leindler [8] and some of the results of Chandra [7] by dropping monotonicity on the elements of the matrix rows (that is, weakening the conditions on the filter, we improve the quality of digital filter). In this paper, a theorem concerning the degree of approximation of the conjugate of a signal (function) f belonging to Lip(ξ(t),r) class by (E,q) summability of conjugate series of its Fourier series has been established which in turn generalizes the results of Chandra [7] and Shukla [18].