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标题：Approximation of Signals (Functions) by Trigonometric Polynomials in <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-6.80586pt;width:22.85px;" id="M1" height="24.112499" version="1.1" viewBox="0 0 22.85 24.112499" width="22.85"> <g transform="matrix(.022,-0,0,-.022,.062,14.638)"><path id="x1D43F" d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z"></path></g> <g transform="matrix(.016,-0,0,-.016,12.862,20.012)"><path id="x1D45D" d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
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作者：M. L. Mittal ; Mradul Veer Singh
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2014
卷号：2014
DOI：10.1155/2014/267383
出版社：Hindawi Publishing Corporation
摘要：Mittal and Rhoades (1999, 2000) and Mittal et al. (2011) have initiated a study of error estimates through trigonometric-Fourier approximation (tfa) for the situations in which the summability matrix does not have monotone rows. In this paper, the first author continues the work in the direction for to be a -matrix. We extend two theorems on summability matrix of Deger et al. (2012) where they have extended two theorems of Chandra (2002) using -method obtained by deleting a set of rows from Cesàro matrix . Our theorems also generalize two theorems of Leindler (2005) to -matrix which in turn generalize the result of Chandra (2002) and Quade (1937).