{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:57:20Z","timestamp":1773147440006,"version":"3.50.1"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,29]],"date-time":"2006-11-29T00:00:00Z","timestamp":1164758400000},"content-version":"vor","delay-in-days":332,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>Mittal and Rhoades (1999\u20132001) and Mittal et al. (2006) have initiated the studies of error estimates <jats:italic>E<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>(<jats:italic>f<\/jats:italic>) through trigonometric Fourier approximations (TFA) for the situations in which the summability matrix <jats:italic>T<\/jats:italic> does not have monotone rows. In this paper, we determine the degree of approximation of a function , conjugate to a periodic function <jats:italic>f<\/jats:italic> belonging to the weighted <jats:italic>W<\/jats:italic>(<jats:italic>L<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub>, <jats:italic>\u03be<\/jats:italic>(<jats:italic>t<\/jats:italic>))\u2010class (<jats:italic>p<\/jats:italic> \u2265 1), where <jats:italic>\u03be<\/jats:italic>(<jats:italic>t<\/jats:italic>) is nonnegative and increasing function of <jats:italic>t<\/jats:italic> by matrix operators <jats:italic>T<\/jats:italic> (without monotone rows) on a conjugate series of Fourier series associated with <jats:italic>f<\/jats:italic>. Our theorem extends a recent result of Mittal et al. (2005) and a theorem of Lal and Nigam (2001) on general matrix summability. Our theorem also generalizes the results of Mittal, Singh, and Mishra (2005) and Qureshi (1981\u20101982) for N\u00f6rlund (<jats:italic>N<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub>)\u2010matrices.<\/jats:p>","DOI":"10.1155\/ijmms\/2006\/53538","type":"journal-article","created":{"date-parts":[[2006,12,27]],"date-time":"2006-12-27T08:10:09Z","timestamp":1167207009000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Approximation of signals (functions) belonging to the weighted <i>W<\/i>(<i>L<\/i><sub><i>p<\/i><\/sub>, <i>\u03be<\/i>(<i>t<\/i>))\u2010class by linear operators"],"prefix":"10.1155","volume":"2006","author":[{"given":"M. L.","family":"Mittal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B. E.","family":"Rhoades","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vishnu Narayan","family":"Mishra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,29]]},"reference":[{"key":"e_1_2_1_1_2","doi-asserted-by":"publisher","DOI":"10.2307\/1989428"},{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1155\/S0161171201005737"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1997.5781"},{"key":"e_1_2_1_4_2","first-page":"77","article-title":"Approximation by matrix means of double Fourier series to continuous functions in two variables","volume":"9","author":"Mittal M. 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L.","year":"2005","journal-title":"Varahmihir Journal of Mathematical Sciences"},{"key":"e_1_2_1_9_2","first-page":"217","article-title":"Approximation of functions (signals) belonging to Lip(?(t), p)-class by means of conjugate Fourier series using linear operators","volume":"47","author":"Mittal M. L.","year":"2005","journal-title":"Indian Journal of Mathematics"},{"key":"e_1_2_1_10_2","volume-title":"Digital Communications","author":"Proakis J. 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