Estimates of the Remainder in Taylor's Theorem Using the Henstock-Kurzweil Integral
نویسندگان
چکیده
منابع مشابه
Estimates of the remainder in Taylor’s theorem using the Henstock–Kurzweil integral
When a real-valued function of one variable is approximated by its n th degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue p-norms in cases where f (n) or f (n+1) are Henstock–Kurzweil integrable. When the only assumption is that f (n) is Henstock–Kurzweil integrable then a modified form of the n th degree Taylor polynomial is used. When the only assumption i...
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We consider the Laplace transform as a Henstock-Kurzweil integral. We give conditions for the existence, continuity and differentiability of the Laplace transform. A Riemann-Lebesgue Lemma is given, and it is proved that the Laplace transform of a convolution is the pointwise product of Laplace transforms.
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In the present paper, measure differential equations involving the distributional Henstock-Kurzweil integral are investigated. Theorems on the existence and structure of the set of solutions are established by using Schauder$^prime s$ fixed point theorem and Vidossich theorem. Two examples of the main results paper are presented. The new results are generalizations of some previous results in t...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2005
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-005-0077-y