A note on the degree of approximation of functions belonging to certain Lipschitz class by almost Riesz means
DOI:
https://doi.org/10.24193/subbmath.2018.3.08Keywords:
Fourier series, degree of approximation, weighted $L^p-$norm, generalized Minkowski inequality, almost Riesz meansAbstract
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.References
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