East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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NEW BOUNDS FOR A PERTURBED GENERALIZED TAYLOR'S FORMULA

  • Cerone, P. (School of Communications and Informatics Victoria University of Technology, Australia) ;
  • Dragomir, S.S. (School of Communications and Informatics Victoria University of Technology, Australia)
  • Published : 2001.12.30
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Abstract

A generalised Taylor series with integral remainder involving a convex combination of the end points of the interval under consideration is investigated. Perturbed generalised Taylor series are bounded in terms of Lebesgue p-norms on $[a,b]^2$ for $f_{\Delta}:[a,b]^2{\rightarrow}\mathbb{R}$ with $f_{\Delta}(t,s)=f(t)-f(s)$.

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