The mean value theorem and analytic functions of a complex variable
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چکیده
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the investigation of the relationship between type a and type b personalities and quality of translation
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Absolute and relative extrema, the mean value theorem and the inverse function theorem for analytic functions on a Levi-Civita field
The proofs of the extreme value theorem, the mean value theorem and the inverse function theorem for analytic functions on the Levi-Civita field will be presented. After reviewing convergence criteria for power series [15], we review their analytical properties [18, 20]. Then we derive necessary and sufficient conditions for the existence of relative extrema for analytic functions and use that ...
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The Mean Value Theorem and Its Consequences
The point (M,f(M)) is called an absolute maximum of f if f(x) ≤ f(M) for every x in the domain of f . The point (m, f(m)) is called an absolute minimum of f if f(x) ≥ f(m) for every x in the domain of f . More than one absolute maximum or minimum may exist. For example, if f(x) = |x| for x ∈ [−1, 1] then f(x) ≤ 1 and there are absolute maxima at (1, 1) and at (−1, 1), but only one absolute mini...
متن کاملOn a mean value theorem in the class of Herglotz functions and its applications
Linear-fractional transformations of the pairs with J-property are considered. Extremal functions from an important subclass obtained in this way are expressed as mean values of extremal functions from another subclass of these linear-fractional transformations. Applications to some spectral and interpolation problems are discussed.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2006
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.11.049