Results 101 to 110 of about 3,513 (190)

A general multidimensional Hermite–Hadamard type inequality

Journal of Mathematical Analysis and Applications, 2009
The classical Hermite-Hadamard inequality states that for a real convex function \(f\) on an interval \([a,b]\), \[ f\biggl({a+b\over2}\biggr)\leq{1\over b-a}\int_a^b f(x)dx\leq{f(a)+f(b)\over2}. \] This may be expressed in probabilistic terms in the form \[ f(E\xi)\leq Ef(\xi)\leq Ef(\xi^*), f\in C_{cx},\eqno(1) \] where \(E\) denotes expected value, \
de la Cal, Jesús, Cárcamo, Javier, Escauriaza, Luis   +2 more
openaire   +1 more source

Improved Hermite–Hadamard Inequality Bounds for Riemann–Liouville Fractional Integrals via Jensen’s Inequality

Fractal and Fractional
This paper derives the sharp bounds for Hermite–Hadamard inequalities in the context of Riemann–Liouville fractional integrals. A generalization of Jensen’s inequality called the Jensen–Mercer inequality is used for general points to find the new and ...
Muhammad Aamir Ali, Wei Liu, Shigeru Furuichi, Michal Fečkan   +3 more
doaj   +1 more source

On q-Hermite-Hadamard Inequalities for Differentiable Convex Functions

Mathematics, 2019
In this paper, we establish some new results on the left-hand side of the q-Hermite−Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et.
Seksan Jhanthanam, Jessada Tariboon, Sotiris K. Ntouyas, Kamsing Nonlaopon   +3 more
doaj   +1 more source

The Hermite–Hadamard Inequality in Higher Dimensions [PDF]

The Journal of Geometric Analysis, 2019
The Hermite-Hadamard inequality states that the average value of a convex function on an interval is bounded from above by the average value of the function at the endpoints of the interval. We provide a generalization to higher dimensions: let $ \subset \mathbb{R}^n$ be a convex domain and let $f: \rightarrow \mathbb{R}$ be a convex function ...
openaire   +3 more sources

On Certain Integral Inequalities Related to Hermite–Hadamard Inequalities

Journal of Mathematical Analysis and Applications, 1999
The authors establish some new Hermite-Hadamard inequalities for real convex functions on \([a,b]\), generalizing known results of this type.
Yang, Gou-Sheng, Tseng, Kuei-Lin
openaire   +2 more sources

Generalized multiplicative h-fractional integrals and derivatives with Hermite-Hadamard inequality

Journal of Inequalities and Applications
In this study, we introduce new generalized multiplicative h-fractional integral and h-fractional derivative operators by employing multiplicative calculus within the framework of fractional analysis.
Umut Bas, Huseyin Yildirim
doaj   +1 more source

Old and New on the Hermite-Hadamard Inequality

Real Analysis Exchange, 2004
This paper is a survey of the results grown up from the Hermite-Hadamard inequality. Both, old and new results are presented, complemented and discussed within this framework. The Hermite-Hadamard inequality is presented in connection with subdifferentials and quadrature formulae; some improvements of it are discussed. Then a short account on classical
Niculescu, Constantin P., Persson, Lars-Erik   +1 more
openaire   +3 more sources

On Fractional Hermite–Hadamard-Type Inequalities for Harmonically s-Convex Stochastic Processes

Fractal and Fractional
In this paper, we investigate Hermite–Hadamard-type inequalities for harmonically s-convex stochastic processes via Riemann–Liouville fractional integrals. We begin by introducing the notion of harmonically s-convex stochastic processes. Subsequently, we
Rabab Alzahrani, Raouf Fakhfakh, Ghadah Alomani, Badreddine Meftah   +3 more
doaj   +1 more source

Ostrowski and Čebyšev type inequalities for interval-valued functions and applications. [PDF]

PLoS One, 2023
Guo J, Zhu X, Li W, Li H.
europepmc   +1 more source

Inequalities of Hermite-Hadamard type for HG-convex functions [PDF]

Issues of Analysis, 2017
Abstract Some inequalities of Hermite-Hadamard type for GA-convex functions defined on positive intervals are given.
openaire   +15 more sources