Results 101 to 110 of about 2,360 (226)

Some refinements of Hadamard inequality

, 2016
碩士如果 f : I → ℝ 為I中的凸函數，則 f( (a+b)/2)≤1/(b-a ) ∫_a^b▒〖f(x)dx ≤ 1/(2 ) [f(a)+f(b)] 〗 (1.1) 恆成立，為眾所週知的Hermite-Hadamard不等式 如果 f為I中的凸函數，是否存在實數 l及L 滿足下列不等式： f((a+b)/2)≤ l ≤1/(b-a ) ∫_a^b▒〖f(x)dx ≤L ≤ 1/(2 ) [f(a)+f(b)] 〗 (1.2 ...
黃維洲;Huang, Wei-Chou
core  

Generalization and Refinements of Hermite-Hadamard's Inequality

Rocky Mountain Journal of Mathematics, 2005
The Hermite-Hadamard inequality can be easily extended to the case of twice differentiable functions \(f\) with bounded second derivative. Precisely, if \(\gamma\leq f^{\prime\prime} \leq\Gamma,\) then \[ \frac{3S_{2}-2\Gamma}{24}(b-a)^{2}\leq\frac{1}{b-a}\int_{a}^{b}f\,dt-f\left( \frac{a+b}{2}\right) \leq\frac{3S_{2}-2\gamma}{24}(b-a)^{2} \] and ...
Qi, Feng, Wei, Zong-Li, Yang, Qiao
openaire   +2 more sources

Refinements of the Hermite-Hadamard Inequality for Convex Functions

, 2015
[[abstract]]Some refinements of the Hermite-Hadamard integral inequality for convex functions and applications for special means are ...
Dragomir,S. S.
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Comparisons of Two Integral Inequalities with Hermite-Hadamard-Jensen's Integral Inequality

, 2005
Certain comparisons of Iyengar-Mahajani’s and Kesava Menon’s integral inequalities with Hermite-Hadamard-Jensen’s integral inequalities are considered and some mistakes in the paper [On certain inequalities by Iyengar and Kesava Menon, Octogon Math ...
Qi, Feng, Yang, Meng-Long
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Advancements in Harmonic Convexity and Its Role in Modern Mathematical Analysis

Journal of Mathematics
Convex functions play an integral part in artificial intelligence by providing mathematical guarantees that make optimization more efficient and reliable.
Sabila Ali, Muhammad Samraiz, Saima Naheed, Miguel Vivas-Cortez   +3 more
doaj   +1 more source

New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex

, 2009
In this note we obtain some inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex.
Dragomir, Sever S, Alomari, Mohammad, Darus, Maslina   +2 more
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On exponentially (h1, h2)-convex functions and fractional integral inequalities related [PDF]

Mathematica Moravica, 2020
In this work the concept of exponentially (h1, h2)-convex function is introduced and using it, the Hermite-Hadamard inequality and some bounds for the right side of this inequality, via Raina's fractional integral operator and generalized convex ...
Vivas-Cortez Miguel, Eliecer Hernández Hernández Jorge, Turhan Sercan   +2 more
doaj  

Generalizations and Refinements of Hermite-Hadamard's Inequality

, 2001
In this article, with the help of concept of the harmonic sequence of polynomials, the well known Hermite-Hadamard’s inequality for convex functions is generalied to the cases with bounded derivatives of n-th order, including the so-called n-convex ...
Qi, Feng, Yang, Qiao, Wei, Zong-Li
core  

A Note on the Ky Fan Inequality

, 2002
The Ky Fan inequality is essentially the assertion that t/(1−t) is log-concave.
Florea, Aurelia, Aurelia Florea, Constantin P. Niculescu, Niculescu, Constantin P   +3 more
core  

Some Integral Inequalities for Local Fractional Integrals

International Journal of Analysis and Applications, 2017
In this paper, firstly we extend some generalization of the Hermite-Hadamard inequality and Bullen inequality to generalized convex functions. Then, we give some important integral inequalities related to these inequalities.
M. Zeki Sarikaya, samet Erden, Hüseyin Budak   +2 more
doaj   +2 more sources