Results 1 to 10 of about 52,246 (269)
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
doaj +4 more sources
Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities
Mathematics, 2021 In this article, we give sharp two-sided bounds for the generalized Jensen functional Jn(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean An(h;p,x). In particular, exact
Slavko Simić, Vesna Todorčević
doaj +4 more sources
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
doaj +2 more sources
On the Equality of Bajraktarević Means to Quasi-Arithmetic Means [PDF]
Results in Mathematics, 2019 AbstractThis paper offers a solution of the functional equation$$\begin{aligned}&\big (tf(x)+(1-t)f(y)\big )\varphi (tx+(1-t)y)\\&\quad =tf(x)\varphi (x)+(1-t)f(y)\varphi (y) \qquad (x,y\in I), \end{aligned}$$(tf(x)+(1-t)f(y))φ(tx+(1-t)y)=tf(x)φ(x)+(1-t)f(y)φ(y)(x,y∈I),where$$t\in \,]0,1[\,$$t∈]0,1[,$$\varphi :I\rightarrow \mathbb {R}$$φ:I→Ris ...
Zsolt Páles, Amr Zakaria
core +10 more sources
Some Mean Values Related to the Quasi-Arithmetic Mean
Journal of Mathematical Analysis and Applications, 2000 Let \(p:\mathbb{R}^{+}\rightarrow \mathbb{R}\) be a strictly monotonic function, \(H\) denote the harmonic mean, \(r\) a real number in \([0,1],\) and \[ t_{n}(\theta)=\left( a^{2n}\cos ^{2}\theta +b^{2n}\sin ^{2}\theta \right) ^{1/n} \quad (n\neq 0). \] The authors study mean values defined by the expressions: \[ M(a,b;p,t_{n})=\frac{1}{H(a,b)}p^{-1 ...
Jeong Sheok Ume
exaly +3 more sources
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
doaj +2 more sources
On the equality of quasi-arithmetic and Lagrangian means
Journal of Mathematical Analysis and Applications, 2011 Six cases of equality are found between quasi-arithmetic and Lagrangian means for continuous monotonic functions.
Zsolt Pales
exaly +3 more sources
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
doaj +3 more sources
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
doaj +1 more source
Refinement of Discrete Lah–Ribarič Inequality and Applications on Csiszár Divergence
Mathematics, 2022 In this paper we give a new refinement of the Lah–Ribarič inequality and, using the same technique, we give a refinement of the Jensen inequality. Using these results, a refinement of the discrete Hölder inequality and a refinement of some inequalities ...
Đilda Pečarić +2 more
doaj +1 more source