One method for proving some classes of exponential analytical inequalities
نویسندگان
چکیده
منابع مشابه
Some improvements of one method for proving inequalities by computer
In the article [17] we consider only the case when n and m are non-negative integer points determined by: n ≥ 1 is the multiplicity of the root x = a, otherwise n = 0 if x = a is not the root; and m ≥ 1 is the multiplicity of the root x = b, otherwise m = 0 if x = b is not the root. In this case, if for the function f(x) at the point x = a there is an approximation of the function by Taylor pol...
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x+ 1 ) < x − 7 4 x+ 9 5 (2) and (x+ 2)Γ(x+ 1) > 9 5 . (3) The previous statement (Lemma 4.1. of the paper [10]) is proved by the approximative formula for the gamma function Γ(x+ 1) by the polynomial of the fifth order: P5(x) = −0.1010678x+0.4245549x−0.6998588x+0.9512363x−0.5748646x+1 (4) which has the numerical bound of the absolute error ε = 5 · 10 for values of argument x∈ [0, 1] [3] (formul...
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Recommended by Andrea Laforgia We consider a numerical method for proving a class of analytical inequalities via mini-max rational approximations. All numerical calculations in this paper are given by Maple computer program. In this section we prove two new inequalities given in Theorems 1.2 and 1.10. While proving these theorems we use a method for inequalities of the form f (x) ≥ 0, for the c...
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In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions, we demonstrate that the considered method generally in practice becomes one heuristic for the verification of inequalities. We give some improvements of the i...
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Let ‖| · ‖| be any give unitarily invariant norm. We obtain some exponential relations in the context of semisimple Lie group. On one hand they extend the inequalities (1) ‖|e‖| ≤ ‖|eReA‖| for all A ∈ Cn×n, where ReA denotes the Hermitian part of A, and (2) ‖|e‖| ≤ ‖|ee‖|, where A and B are n×n Hermitian matrices. On the other hand, the inequalities of Weyl, Ky Fan, Golden-Thompson, Lenard-Thom...
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ژورنال
عنوان ژورنال: Filomat
سال: 2018
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1820921m