Results 81 to 90 of about 3,513 (190)
Implications between approximate convexity properties and approximate Hermite-Hadamard inequalities
, 2012 In this paper, the connection between the functional inequalities $$ f\Big(\frac{x+y}{2}\Big)\leq\frac{f(x)+f(y)}{2}+\alpha_J(x-y) \qquad (x,y\in D)$$ and $$ \int_0^1f\big(tx+(1-t)y\big)\rho(t)dt \leq\lambda f(x)+(1-\lambda)f(y) +\alpha_H(x-y) \qquad (x ...
Makó, Judit, Páles, Zsolt
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Green’s Function Approach to Hermite–Hadamard–Mercer Type Fractional Inequalities and Applications
Journal of Mathematics, Volume 2026, Issue 1, 2026.The Hermite–Hadamard–Mercer (HHM) inequality, existing in two well‐established forms, plays a fundamental role in mathematical analysis. This inequality is characterized by three distinct components—namely, the left, middle, and right terms. This study is concerned to obtain novel generalized and refined HHM fractional inequalities by employing for the
Muhammad Zafran +6 more
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Hermite-Hadamard type inequalities for Wright-convex functions of several variables
, 2014 We present Hermite--Hadamard type inequalities for Wright-convex, strongly convex and strongly Wright-convex functions of several variables defined on ...
Wasowicz, Sz., Śliwińska, D.
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 12567-12576, August 2025.ABSTRACT The significance of the Jensen inequality stems from its impactful and compelling outcomes. As a generalization of classical convexity, it plays a key role in deriving other well‐known inequalities such as Hermite–Hadamard, Hölder, Minkowski, arithmetic‐geometric, and Young's inequalities.
İzzettin Demir
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Hermite-Hadamard-Fejér Type Inequalities for Preinvex Functions Using Fractional Integrals
Mathematics, 2019 In this paper, we have established the Hermite−Hadamard−Fejér inequality for fractional integrals involving preinvex functions. The results presented here provide new extensions of those given in earlier works as the weighted estimates ...
Sikander Mehmood +2 more
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Hermite-Hadamard type inequalities for subadditive functions
AIMS Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Quantum Ghost Imaging by Sparse Spatial Mode Reconstruction
Advanced Quantum Technologies, Volume 8, Issue 5, May 2025.Hermite–Gaussian spatial modes are used in quantum ghost imaging for enhanced image reconstruction, by exploiting modal sparsity. By leveraging structured light as a basis for imaging, time‐efficient and high resolution quantum ghost imaging is achieved, paving the way for breakthroughs in low‐light, biological science applications.
Fazilah Nothlawala +4 more
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International Journal of Mathematics and Mathematical Sciences, 2022 In order to be able to study cosmic phenomena more accurately and broadly, it was necessary to expand the concept of calculus. In this study, we aim to introduce a new fractional Hermite–Hadamard–Mercer’s inequality and its fractional integral type ...
Tariq A. Aljaaidi, Deepak B. Pachpatte
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On Hadamard Type Integral Inequalities for nonconvex Functions [PDF]
, 2013 In this paper, we extend some estimates of the right and left hand side of a Hermite-Hadamard type inequality for nonconvex functions whose derivatives absolute values are \Phi-convex and quasi-\Phi-convex was introduced by Noor in Noor1.Comment ...
Communicated Murat Tosun +3 more
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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
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