Hermite-Hadamard-Fejér Inequalities for Preinvex Functions on Fractal Sets [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, for generalised preinvex functions, new estimates of the Fej\'{e}r-Hermite-Hadamard inequality on fractional sets $\mathbb{R}^{\rho }$ are given in this study.
Sikander Mehmood, Fiza Zafar
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Interpolation inequalities between Sobolev and Morrey-Campanato spaces: A common gateway to concentration-compactness and Gagliardo-Nirenberg interpolation inequalities [PDF]
, 2013 We prove interpolation estimates between Morrey-Campanato spaces and Sobolev spaces. These estimates give in particular concentration-compactness inequalities in the translation-invariant and in the translation- and dilation-invariant case.
Van Schaftingen, Jean
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Weighted Norm Inequalities for Fractional Integrals [PDF]
Proceedings of the American Mathematical Society, 1975 A simpler proof of an inequality of Muckenhoupt and Wheeden is given. Let T α f ( x ) = ∫ f ( y ) | x − y | α
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Refinements of some integral inequalities for unified integral operators
Journal of Inequalities and Applications, 2021 In this paper we are presenting the refinements of integral inequalities established for convex functions. Consequently, we get refinements of several fractional integral inequalities for different kinds of fractional integral operators.
Chahn Yong Jung +4 more
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On Fractional Inequalities Using Generalized Proportional Hadamard Fractional Integral Operator
Axioms, 2022 The main objective of this paper is to use the generalized proportional Hadamard fractional integral operator to establish some new fractional integral inequalities for extended Chebyshev functionals.
Vaijanath L. Chinchane +4 more
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Fractional Integrals and Generalized Olsen Inequalities
Kyungpook mathematical journal, 2009 Summary: Let \(T_\rho\) be the generalized fractional integral operator associated to a function \(\rho:(0,\infty)\to(0,\infty)\), as defined in [\textit{E. Nakai}, Taiwanese J. Math. 5, No.~3, 587--602 (2001; Zbl 0990.26007)]. For a function \(W\) on \(\mathbb R^n\), we be interested in the boundedness of the multiplication operator \(f\mapsto W\cdot ...
Hendra Gunawan, Eridani
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Error Bounds for Fractional Integral Inequalities with Applications
Fractal and FractionalFractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson’s type estimates by employing a differentiable ...
N. A. Alqahtani +4 more
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Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications
Fractal and Fractional, 2021 In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an
H. Srivastava +4 more
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Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group
, 2016 We prove Hardy inequalities for the conformally invariant fractional powers of the sublaplacian on the Heisenberg group $\mathbb{H}^n$. We prove two versions of such inequalities depending on whether the weights involved are non-homogeneous or ...
Roncal, L., Thangavelu, S.
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On new fractional integral inequalities for p-convexity within interval-valued functions
Advances in Differential Equations, 2020 This work mainly investigates a class of convex interval-valued functions via the Katugampola fractional integral operator. By considering the p-convexity of the interval-valued functions, we establish some integral inequalities of the Hermite–Hadamard ...
T. Abdeljawad +3 more
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