Approximation of signals belonging to generalized Lipschitz class using -summability mean of Fourier series

• Main Authors: Tejaswini Pradhan, Susanta Kumar Paikray, Umakanta Misra
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2016-12-01
• Series: Cogent Mathematics
• Subjects: degree of approximation; Fourier series; weighted $ W(L_{r},\xi (t)) $-class; $ (\overline{N}, p_{n}, q_{n})(E, s) $-mean; $ (\overline{N} p_{n}q_{n})(E, s) $-mean; Lebesgue integral
• Online Access: http://dx.doi.org/10.1080/23311835.2016.1250343
• ISSN: 2331-1835

Degree of approximation of functions of different classes has been studied by several researchers by different summability methods. In the proposed paper, we have established a new theorem for the approximation of a signal (function) belonging to the $ W(L_{r},\xi (t)) $-class by $ (\overline{N},p_{n},q_{n})(E,s) $-product summability means of a Fourier series. The result obtained here, generalizes several known theorems.