In this paper we will point out a similar inequality to hadamard's for h-convex function defined on a disk. Some mappings connected with this inequality and related results are also obtained. (C) 2014 Elsevier Inc...
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In this paper we will point out a similar inequality to hadamard's for h-convex function defined on a disk. Some mappings connected with this inequality and related results are also obtained. (C) 2014 Elsevier Inc. All rights reserved.
This paper develops a novel Milne inequality for third-differentiable and h-convex functions using Riemann integrals. Furthermore, new Milne inequalities are proposed utilizing a summation parameter p >= 1\document...
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This paper develops a novel Milne inequality for third-differentiable and h-convex functions using Riemann integrals. Furthermore, new Milne inequalities are proposed utilizing a summation parameter p >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p\geq 1$\end{document} for s-convexity, convexity, and P-functions class. We examine cases when the third derivative functions are also bounded and Lipschitzian.
In this paper, we first prove a generalized fractional version of hermite-hadamard-Mercer type inequalities using h-convex functions by means of psi-hilfer fractional integral operators. Then, we give new identities o...
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In this paper, we first prove a generalized fractional version of hermite-hadamard-Mercer type inequalities using h-convex functions by means of psi-hilfer fractional integral operators. Then, we give new identities of this type with special functions depending on psi. Moreover, we establish some new fractional integral inequalities connected with the right- and left-hand sides of hermite-hadamard-Mercer inequalities involving differentiable mappings whose absolute values of the derivatives are h-convex. For the development of these novel integral inequalities, we utilize h-Mercer inequality and h & ouml;lder's integral inequality. These results offer the significant advantage of being convertible into classical integral inequalities and Riemann-Liouville fractional integral inequalities for convexfunctions, s-convexfunctions, and P-convexfunctions.
This article introduces the Giaccardi inequality using isotonic linear functionals and h-convexity. This work includes both discrete and integral variants of this inequality. The important Petrovi & cacute;inequal...
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This article introduces the Giaccardi inequality using isotonic linear functionals and h-convexity. This work includes both discrete and integral variants of this inequality. The important Petrovi & cacute;inequality is deduced as a special case. For some applications, the established inequalities are extended to time scales.
A mapping Mg(t) is considered to obtain some preliminary results and a new trapezoidal form of Fejer inequality related to the h-convex functions. Furthermore the obtained results are applied to achieve some new inequ...
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A mapping Mg(t) is considered to obtain some preliminary results and a new trapezoidal form of Fejer inequality related to the h-convex functions. Furthermore the obtained results are applied to achieve some new inequalities in connection with special means, random variable and trapezoidal formula.
In this paper we prove the hermite-hadamard-Fejer inequalities for an h-convex function and we point out the results for some special classes of functions. Also, some generalization of the hermite-hadamard inequalitie...
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In this paper we prove the hermite-hadamard-Fejer inequalities for an h-convex function and we point out the results for some special classes of functions. Also, some generalization of the hermite-hadamard inequalities and some properties of functions h and F which are naturally joined to the h-convex function are given. Finally, applications on p-logarithmic mean and mean of the order p are obtained. (C) 2009 Elsevier Ltd. All rights reserved.
In this paper, we state some characterizations of h-convex function defined on a convex set in a linear space. By doing so, we extend the Jensen-Mercer inequality for h-convex function. We present the concept of opera...
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In this paper, we state some characterizations of h-convex function defined on a convex set in a linear space. By doing so, we extend the Jensen-Mercer inequality for h-convex function. We present the concept of operator h-convex functions and give some operator versions of Jensen and Jensen-Mercer type inequalities for some classes of operator h-convex functions and unital positive linear maps. Finally, we introduce the complementary inequality of Jensen's inequality for h-convex functions.
We introduce the notion of strongly h-convex functions (defined on a normed space) and present some properties and representations of suchfunctions. We obtain a characterization of inner product spaces involving the ...
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We introduce the notion of strongly h-convex functions (defined on a normed space) and present some properties and representations of suchfunctions. We obtain a characterization of inner product spaces involving the notion of strongly h-convex functions. Finally, a hermite-hadamard-type inequality for strongly h-convex functions is given.
In this paper, we obtain some hermite-hadamard type inequalities for h-convex functions. Also, some applications to special means of real numbers are given. The results presented here provide extensions of those given...
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In this paper, we obtain some hermite-hadamard type inequalities for h-convex functions. Also, some applications to special means of real numbers are given. The results presented here provide extensions of those given in earlier works.
We derive some properties and results for a new extended class of convexfunctions, generalized strongly modified h-convex functions. Moreover, we discuss Schur-type, hermite-hadamard-type, and Fejer-type inequalities...
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We derive some properties and results for a new extended class of convexfunctions, generalized strongly modified h-convex functions. Moreover, we discuss Schur-type, hermite-hadamard-type, and Fejer-type inequalities for this class. The crucial fact is that this extended class has awesome properties similar to those of convexfunctions.
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