Kyungpook Mathematical Journal

  • 제50권4호
  • /
  • Pages.545-556
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  • 2010
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On Approximation of Functions Belonging to Lip(α, r) Class and to Weighted W(Lr,ξ(t)) Class by Product Mean

  • Nigam, Hare Krishna (Department of Mathematics, Faculty of Engineering and Technology, Mody Institute of Technology and Science (Deemed University)) ;
  • Sharm, Ajay (Department of Mathematics, Faculty of Engineering and Technology, Mody Institute of Technology and Science (Deemed University))
  • 투고 : 2010.01.21
  • 심사 : 2010.10.28
  • 발행 : 2010.12.31
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초록

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

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참고문헌

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