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Hermite-Hadamard Type Inequalities for Quasi-Convex Functions via Katugampola Fractional Integrals
International Journal of Analysis and Applications, 2018 The paper deals with quasi-convex functions, Katugampola fractional integrals and Hermite-Hadamard type integral inequalities. The main idea of this paper is to present new Hermite-Hadamard type inequalities for quasi-convex functions using Katugampola ...
Erhan Set, Ilker Mumcu
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Journal of Inequalities and Applications, 2019 In this paper, we establish a new Hermite–Hadamard inequality involving left-sided and right-sided ψ-Riemann–Liouville fractional integrals via convex functions.
Kui Liu, JinRong Wang, Donal O’Regan
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New Estimates for Exponentially Convex Functions via Conformable Fractional Operator
Fractal and Fractional, 2019 In this paper, we derive a new Hermite–Hadamard inequality for exponentially convex functions via α -fractional integral. We also prove a new integral identity.
Saima Rashid +2 more
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On Some Generalized Fractional Integral Inequalities for p-Convex Functions
Fractal and Fractional, 2019 In this paper, firstly we have established a new generalization of Hermite−Hadamard inequality via p-convex function and fractional integral operators which generalize the Riemann−Liouville fractional integral operators introduced by Raina ...
Seren Salaş +3 more
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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 +2 more
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Fractal and FractionalThis 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 +3 more
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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 +3 more
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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 ...
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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
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Generalized multiplicative h-fractional integrals and derivatives with Hermite-Hadamard inequality
Journal of Inequalities and ApplicationsIn 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
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