Abstract
In this paper, we determine the degree of approximation of functions belonging to \( L[0,\infty )\) by the Hausdorff means of its Fourier–Laguerre series at \(x=0.\) Our theorem extends some of the recent results of Nigam and Sharma [A study on degree of approximation by (E, 1) summability means of the Fourier–Laguerre expansion, Int. J. Math. Math. Sci. (2010), Art. ID 351016, 7], Krasniqi [On the degree of approximation of a function by (C, 1)(E, q) means of its Fourier–Laguerre series, International Journal of Analysis and Applications 1 (2013), 33–39] and Sonker [Approximation of Functions by (C, 2)(E, q) means of its Fourier–Laguerre series, Proceeding of ICMS-2014 ISBN 978-93-5107-261-4:125–128.] in the sense that the summability methods used by these authors have been replaced by the Hausdorff matrices.
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Garabedian, H.L.: Hausdorff matrices. Am. Math. Monthly 46(7), 390–410
Gupta, D.P.: Degree of approximation by Cesàro means of Fourier-Laguerre expansions. Acta Sci. Math. (Szeged) 32, 255–259 (1971)
Hardy, G.H.: Divergent Series. Oxford at the Clarendon Press (1949)
Krasniqi, X.Z.: On the degree of approximation of a function by \((C,1)(E, q)\) means of its Fourier-Laguerre series. Int. J. Anal. Appl. 1, 33–39 (2013)
Nigam, H.K, Ajay, S.: A study on degree of approximation by \((E,1)\) summability means of the Fourier-Laguerre expansion. Int. J. Math. Math. Sci. (Art. ID 351016), 7 (2010)
Rhoades, B.E.: Commutants for some classes of Hausdorff matrices. Proc. Am. Math. Soc. 123(9), 2745–2755 (1995)
Rhoades, B.E.: On the degree of approximation of functions belonging to the weighted \((L^{p},\xi (t))\) class by Hausdorff means. Tamkang J. Math. 32(4), 305–314 (2001)
Rhoades, B.E., Kevser, O., Albayrak Inc.: On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its Fourier series. Appl. Math. Comput. 217(16), 6868–6871 (2011)
Szegö, G.: Orthogonal polynomials. Am. Math. Soc. Colloquium Publ. 23, (1939)
Sonker, S.: Approximation of Functions by \((C, 2)(E, q)\) means of its Fourier-Laguerre series. Proceeding of ICMS-2014, (2014). ISBN:978-93-5107-261-4:125–128
Singh, U., Sonker, S.: Trigonometric approximation of signals (functions) belonging to weighted \((L^p,\xi (t))\)-class by Hausdorff means. J. Appl. Funct. Anal. 8(1), 37–44 (2013)
Acknowledgments
The authors express their sincere gratitude to the reviewers for their valuable suggestions for improving the paper. This research is supported by the Council of Scientific and Industrial Research (CSIR), New Delhi, India (Award No.- 09/143(0821)/2012-EMR-I) in the form of fellowship to the first author.
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Saini, S., Singh, U. (2015). Degree of Approximation of \(f\in L[0,\infty )\) by Means of Fourier–Laguerre Series. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_16
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DOI: https://doi.org/10.1007/978-81-322-2485-3_16
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