A note on the degree of approximation of functions belonging to certain Lipschitz class by almost Riesz means

Uaday Singh, Arti Rathore

Abstract


The problem of obtaining degree of approximation for the $2\pi-$periodic functions in the weighted Lipschitz class $W(L^p,\xi(t))~(p\geq 1)$ by Riesz means of the Fourier series have been studied by various investigators under $L^p-$norm. Recently, Deepmala and Piscoran [Approximation of signals(functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series, J. Inequal. Appl., (2016), 2016:163. DOI 10.1186/s13660-016-1101-5] obtained a result on degree of approximation for weighted  Lipschitz class by Riesz means. In this note, we extend this study to the weighted $L^p-$norm which in turn improves some of the previous results. We also derive some corollaries from our result.

Keywords


Fourier series; degree of approximation; weighted $L^p-$norm; generalized Minkowski inequality; almost Riesz means

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2018.3.08

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