Journal ArticleDOI
Multiplicative properties of real functions with applications to classical functions
Carlos Finol,Marek Wójtowicz +1 more
TLDR
In this paper, the characterisation of geometrically convex and concave functions defined on (0,A] or (A, ∞) with multiplicative conditions was studied and unified proofs of some known and new inequalities were obtained.Abstract:
From the characterisation of geometrically convex and geometrically concave functions defined on (0,A] or \( [A,\infty) \) with \( A > 0 \), by means of their multiplicative conditions, we obtain unified proofs of some known and new inequalities. Functions of class C2 and strictly increasing on (a,b) fulfil some kind of supermultiplicativity and superadditivity. We have obtained a new constant determining the intervals of sub- and supermultiplicativity for the log function.read more
Citations
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Journal ArticleDOI
An introduction to classical real analysis, by Karl R. Stromberg. Pp 575. $29·95. 1981. ISBN 0-534-98012-0 (Wadsworth)
TL;DR: In this paper, the elementary transcendental functions of the Trigonometric series and infinite products are defined and discussed. But the authors do not discuss the relationship between these functions and the infinite series.
Journal ArticleDOI
A subadditive property of the gamma function
Horst Alzer,Stephan Ruscheweyh +1 more
TL;DR: In this paper, it was shown that the function x↦(Γ(x))α is subadditive on (0, ∞) if and only if α ∗ ⩽α⩽0.
Journal ArticleDOI
Turning Up the Heat: The Discouraging Effect of Competition in Contests
TL;DR: The authors study contests in which contestants are homogeneous and have convex effort costs and find that increasing contest competitiveness, by making prizes more unequal, scaling up the competition, or adding new contestants, always discourages effort.
Journal ArticleDOI
Inequalities for Euler's gamma function
TL;DR: In this article, the gamma function was shown to be log-convex on (0, ∞) for all x, y > 0 if and only if 1 ≤ a ≤ a ≥ a 0.
Journal ArticleDOI
On generalized strongly modified h-convex functions
TL;DR: In this article, a new extended class of convex functions, generalized strongly modified h-convex functions (H-Convex), was introduced, which has properties similar to those of the original convex function.
References
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Book
The Theory of the Riemann Zeta-Function
TL;DR: The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it one of the most important tools in the study of prime numbers as mentioned in this paper.
Book ChapterDOI
Functions of a Complex Variable
TL;DR: In this paper, a theory of complex-valued functions of a complexvalued argument is presented, which contains some remarkably powerful results which are applicable to a variety of problems, such as the Fourier series expansion.
Book
An Introduction to the Theory of Functional Equations and Inequalities: Cauchy's Equation and Jensen's Inequality
TL;DR: In this article, Cauchy's Functional Equation and Jensen's Inequality are used to show the boundedness and continuuity of Convex Functions and Additive Functions.
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The area measure of log-concave functions and related inequalities
Andrea Colesanti,Ilaria Fragalà +1 more