Results 61 to 70 of about 446 (83)
Polynomial selections and separation by polynomials [PDF]
Studia Math. 120 (1996), 75-82, 2008 Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex functions of higher order. Another application is some Hyers-Ulam-stability-type result.
arxiv
Gautchi's ratio and the Volume of the unit ball in R^n [PDF]
arXiv, 2009 Let Omega(n) be the volume of the unit ball in R^n. We formulate as an infinite product the gamma function ratio gamma(x+1/2)/gamma(x),x>0, which allows us to reproduce and /or produce a variety of formulas and inequalities, some of them seemingly new, concerning Omega(n-1)/Omega(n),and (Omega(n))^2/Omega(n-1)Omega(n+1)
arxiv
Dominance in the family of Sugeno-Weber t-norms [PDF]
arXiv, 2010 The dominance relationship between two members of the family of Sugeno Weber t-norms is proven by using a quantifer elimination algorithm. Further it is shown that dominance is a transitive, and therefore also an order relation, on this family of t-norms.
arxiv
The Proof of Alzer's Conjecture on Generalized Logarithmic Mean [PDF]
arXiv, 2011 In 1987, Alzer posed a conjecture on generalized logarithmic mean, which was introduced by Stolarsky in 1975. To prove Alzer's conjecture, Lou posed a conjecture on generalized inverse harmonic mean in 1995. By proving Lou's conjecture, the paper yields Alzer's conjecture finally.
arxiv
A short extension of two of Spira's results [PDF]
J. Math. Inequal. 2015, vol. 9, no. 3 pp. 795-798, 2013 Two inequalities concerning the symmetry of the zeta-function and the Ramanujan $\tau$-function are improved through the use of some elementary considerations.
arxiv
Some refinements of Hermite-Hadamard inequality and an open problem [PDF]
arXiv, 2016 We presented here a refinement of Hermite-Hadamard inequality as a linear combination of its end-points. The problem of best possible constants is closely connected with well known Simpson's rule in numerical integration. It is solved here for a wide class of convex functions, but not in general. Some supplementary results are also given.
arxiv
Certain inequalities involving the k-Struve function [PDF]
arXiv, 2016 We aim to introduce a $\mathtt{k}$-Struve function and investigate its various properties, including mainly certain inequalities associated this function. One of the inequalities given here is pointed out to be related to the so-called classical Tur\'an type inequality. We also present a differential equation, several recurrence relations, and integral
arxiv
Monotonicity patterns and functional inequalities for classical and generalized Wright functions [PDF]
arXiv, 2017 In this paper our aim is to present the completely monotonicity and convexity properties for the Wright function. As consequences of these results, we present some functional inequalities. Moreover, we derive the monotonicity and log-convexity results for the generalized Wright functions.
arxiv
Approximation and bounds for the Wallis ratio [PDF]
arXiv, 2017 In this paper, we present an improved continued fraction approximation of the Wallis ratio. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the double-side inequality related to this approximation.
arxiv
Gasper's determinant theorem, revisited [PDF]
arXiv, 2018 Let $n \ge 2$ be a natural number, $M$ a real $n \times n$ matrix, $s$ the sum of the entries of $M$ and $q$ the sum of their squares. With $\alpha := s/n$ and $\beta := q/n$, Gasper's determinant bound says that $ |\det M| \le \beta^{n/2}$, and in case of $\alpha^2 \ge \beta$: $$|\det M| \le |\alpha| \left(\frac{n\beta-\alpha^2}{n-1}\right)^{\frac{n-1}
arxiv