Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters [PDF]
Journal of Inequalities and Applications, 2017 In the article, we present the best possible parameters λ = λ ( p ) $\lambda=\lambda (p)$ and μ = μ ( p ) $\mu=\mu(p)$ on the interval [ 0 , 1 / 2 ] $[0, 1/2]$ such that the double inequality G p [ λ a + ( 1 − λ ) b , λ b + ( 1 − λ ) a ] A 1 − p ( a , b )
Wei-Mao Qian, Yu-Ming Chu
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On approximating the quasi-arithmetic mean [PDF]
Journal of Inequalities and Applications, 2019 In this article, we prove that the double inequalities α1[7C(a,b)16+9H(a,b)16]+(1−α1)[3A(a,b)4+G(a,b)4]
Tie-Hong Zhao +3 more
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On Kedlaya-type inequalities for weighted means [PDF]
Journal of Inequalities and Applications, 2018 In 2016 we proved that for every symmetric, repetition invariant and Jensen concave mean M $\mathscr{M}$ the Kedlaya-type inequality A(x1,M(x1,x2),…,M(x1,…,xn))≤M(x1,A(x1,x2),…,A(x1,…,xn)) $$ \mathscr{A} \bigl(x_{1},\mathscr{M}(x_{1},x_{2}), \ldots ...
Zsolt Páles, Paweł Pasteczka
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On the equality of Bajraktarevi\'c means to quasi-arithmetic means [PDF]
Results in Mathematics, 2019 This paper offers a solution of the functional equation $$ \big(tf(x)+(1-t)f(y)\big)\varphi(tx+(1-t)y)=tf(x)\varphi(x)+(1-t)f(y)\varphi(y) \qquad(x,y\in I), $$ where $t\in\,]0,1[\,$ is a fixed number, $\varphi:I\to\mathbb{R}$ is strictly monotone ...
Páles, Zsolt, Zakaria, Amr
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Fast Proxy Centers for the Jeffreys Centroid: The Jeffreys–Fisher–Rao Center and the Gauss–Bregman Inductive Center [PDF]
EntropyThe symmetric Kullback–Leibler centroid, also called the Jeffreys centroid, of a set of mutually absolutely continuous probability distributions on a measure space provides a notion of centrality which has proven useful in many tasks, including ...
Frank Nielsen
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On the Jensen–Shannon Symmetrization of Distances Relying on Abstract Means
Entropy, 2019 The Jensen–Shannon divergence is a renowned bounded symmetrization of the unbounded Kullback–Leibler divergence which measures the total Kullback–Leibler divergence to the average mixture distribution.
Frank Nielsen
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On axiomizing and extending the quasi-arithmetic mean [PDF]
, 2018 Quasi-arithmetic means contain many other mean value concepts such as the arithmetic, the geometric or the harmonic mean as special cases. Treating quasi-arithmetic means as sequences of mappings from I^n into I (for some real interval I) this paper ...
Hansen, Maurice
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Sugeno Integral for Hermite–Hadamard Inequality and Quasi-Arithmetic Means
Annales Mathematicae Silesianae, 2023 In this paper, we present the Sugeno integral of Hermite–Hadamard inequality for the case of quasi-arithmetically convex (q-ac) functions which acts as a generator for all quasi-arithmetic means in the frame work of Sugeno integral.
Nadhomi Timothy
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Fractional Integral Inequalities for Some Convex Functions [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 In this paper, we obtained several new integral inequalities using fractional Riemann-Liouville integrals for convex s-Godunova-Levin functions in the second sense and for quasi-convex functions.
B.R. Bayraktar, A.Kh. Attaev
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Stochastic Order and Generalized Weighted Mean Invariance
Entropy, 2021 In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines ...
Mateu Sbert +3 more
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