Nonconvex functions and separation by power means
TLDR
In this paper, it was shown that for a nonconvex function defined on a real interval, there exists a point where this function behaves like a strictly concave function.Abstract:
In this note we show that, for a nonconvex function defined on a real interval, there exists a point where this function behaves like a strictly concave function. Due to this result, global convexity can be characterized as pointwise convexity everywhere. As an application, a necessary and sufficient condition for the separability of quasiarithmetic means with power means is obtained. Mathematics subject classification (1991): Primary 26A51, 26B25.read more
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Gauss-composition of means and the solution of the Matkowski-Sutô problem
Zoltán Daróczy,Zsolt Páles +1 more
TL;DR: In this paper, the Matkowski-Sutô problem is completely solved, that is, continuous and strictly monotonic functions φ and ψ defined on an open real interval I are determined such that the functional equation (1) φ−1 φ(x) + φ (y) 2 + ψ− 1 ψ(x + y) 2 = x + y + y holds for all x, y ∈ I. The main result obtained is a generalization of that of Sutô (1914) and Matkowski (1999
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Hermite–Hadamard inequality for convex stochastic processes
TL;DR: In this paper, the Hermite-Hadamard inequality was extended to convex stochastic processes, and the authors extended the classical Hermite Hadamard inequalities to the convex case.
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Characterizations of convexity via Hadamard's inequality
Mihály Bessenyei,Zsolt Páles +1 more
TL;DR: In this paper, the Hermite-Hadamard inequality is applied to generalized convexity induced by two-dimensional Chebyshev systems, and a characterization theorem of continuous, non-convex functions is presented.
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Hermite¿Hadamard inequalities for generalized convex functions
Mihály Bessenyei,Zsolt Páles +1 more
TL;DR: In this article, the Hermite-Hadamard type inequalities for generalized convex functions were established for Tcheby-chev systems, based on moment spaces induced by Tchebyschev systems.
Hermite-Hadamard-type Inequalitites for Generalized Convex Functions
TL;DR: In this article, the authors extend the Hermite-Hadamard inequality to the case when the convexity notion is induced by a Chebyshev system, which is the case in this paper.
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