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1.
In this paper, we introduce the notion of coordinated harmonically convex functions. We derive some new integral inequalities of Hermite–Hadamard type for coordinated Harmonically convex functions. The interested readers are encouraged to find the applications of harmonically convex functions in pure and applied sciences. 相似文献
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We obtain some new inequalities of Hermite–Hadamard type. We consider functions that have convex or generalized convex derivative. Additional inequalities are proven for functions whose second derivative in absolute values are convex. Applications of the main results are presented.
相似文献4.
Hasan Kara Muhammad Aamir Ali Hüseyin Budak 《Mathematical Methods in the Applied Sciences》2021,44(1):104-123
In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals. 相似文献
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Ukrainian Mathematical Journal - We provide a unified approach to getting Hermite–Hadamard inequalities for functions with convex absolute values of the second derivatives via the... 相似文献
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A. G. Ghazanfari 《Complex Analysis and Operator Theory》2016,10(8):1695-1703
In this paper, we shall offer two inequalities for differentiable mappings which the induced maps by them on the set of Hermitian operators are operator convex. we establish some estimates of the right hand side of a Hermite–Hadamard type inequality in which such functions are involved. 相似文献
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Hermite–Hadamard’s type inequalities for convex functions of selfadjoint operators in Hilbert spaces
S.S. Dragomir 《Linear algebra and its applications》2012,436(5):1503-1515
Some Hermite–Hadamard’s type inequalities for convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications in relation with the celebrated Hölder–McCarthy’s inequality for positive operators and Ky Fan’s inequality for real numbers are given as well. 相似文献
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In the paper the authors introduce concepts of the m- and (α, m)-geometrically convex functions and establish some inequalities of Hermite–Hadamard type for these classes of functions. 相似文献
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Muhammad Adil Khan Shahid Khan Samet Erden Muhammad Samraiz 《Mathematical Methods in the Applied Sciences》2022,45(1):36-48
There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory. 相似文献
10.
Yuki Seo 《Linear algebra and its applications》2000,320(1-3)
As a converse of the arithmetic–geometric mean inequality, W. Specht [Math. Z. 74 (1960) 91–98] estimated the ratio of the arithmetic mean to the geometric one. In this paper, we shall show complementary inequalities to the matricial generalization of Oppenheim's inequality and the Golden–Thompson type inequalities on the Hadamard product by T. Ando [Linear Algebra Appl. 26 (1979) 203; Linear Algebra Appl. 241–243 (1996) 105], in which Specht's ratio plays an important role. As an application, we shall obtain a complementary inequality to the Hadamard determinant inequality. 相似文献
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Mediterranean Journal of Mathematics - In this paper, we illustrate the Hermite–Hadamard inequality for convex and strongly convex functions defined on hemispheres. A version of... 相似文献
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We consider a family of two-point quadrature formulae and establish sharp estimates for the remainders under various regularity conditions. Improved forms of certain integral inequalities due to Hermite and Hadamard, Iyengar, Milovanovi
and Pecari
, and others are obtained as special cases. Our results can also be interpreted as analogues to a theorem of Ostrowski on the deviation of a function from its averages. Furthermore, we establish a generalization of a result of Fink concerning Lp estimates for the remainder of the trapezoidal rule and present the best constants in the error bounds. 相似文献
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Aequationes mathematicae - In this paper the concept of symmetrized convex stochastic processes is introduced. Some characterizations involving Hermite–Hadamard type inequalities and a... 相似文献
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In the paper, we introduce a new concept ‘geometrically quasi-convex function’ and establish some Hermite–Hadamard type inequalities for functions whose derivatives are of geometric quasi-convexity. 相似文献
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By the use of Hermite–Hadamard’s inequality and weight functions, a half-discrete Hilbert-type inequality in the whole plane with the kernel of hyperbolic cotangent function and multi-parameters is given. The constant factor related to the Riemann zeta function is proved to be the best possible. The equivalent forms, two kinds of particular inequalities, the operator expressions and some equivalent reverses are considered. 相似文献
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Motivated by the well-known Heinz norm inequalities, in this article we study the corresponding Heinz operator inequalities. We derive the whole series of refinements of these operator inequalities, first with the help of the well-known Hermite–Hadamard inequality, and then, utilizing the parametrized family of the so-called Heron means. In such a way, we obtain improvements of some recent results, known from the literature. 相似文献
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Dawid Kotrys 《Aequationes Mathematicae》2013,86(1-2):91-98
Strongly convex stochastic processes are introduced. Some well-known results concerning convex functions, like the Hermite–Hadamard inequality, Jensen inequality, Kuhn theorem and Bernstein–Doetsch theorem are extended to strongly convex stochastic processes. 相似文献
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We establish a new refinement of the right-hand side of the Hermite–Hadamard inequality for convex functions of several variables defined on simplices. 相似文献
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In this work we establish some new Hermite–Hadamard-type inequalities for convex functions and give several applications for special means. 相似文献