scholarly journals Functions Like Convex Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Zlatko Pavić
Keyword(s):  
Convex Functions ◽  
Convex Sets ◽  
Jensen’S Inequality ◽  
Convexity Property ◽  
Linear Functionals ◽  
Jensen's Inequality ◽  
Positive Linear Functionals ◽  
Functional Forms ◽  
Common Center ◽  
The Common

The paper deals with convex sets, functions satisfying the global convexity property, and positive linear functionals. Jensen's type inequalities can be obtained by using convex combinations with the common center. Following the idea of the common center, the functional forms of Jensen's inequality are considered in this paper.

scholarly journals The Applications of Functional Variants of Jensen's Inequality

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Zlatko Pavić
Keyword(s):  
Convex Functions ◽  
Functional Form ◽  
Jensen’S Inequality ◽  
Linear Functionals ◽  
Jensen's Inequality ◽  
Positive Linear Functionals ◽  
Functional Variants ◽  
Several Variables

The paper is inspired by McShane's results on the functional form of Jensen's inequality for convex functions of several variables. The work is focused on applications and generalizations of this important result. At that, the generalizations of Jensen's inequality are obtained using the positive linear functionals.

scholarly journals Application of Functionals in Creating Inequalities

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Zlatko Pavić ◽  
Shanhe Wu ◽  
Vedran Novoselac
Keyword(s):  
Convex Functions ◽  
Functional Form ◽  
Closed Interval ◽  
Jensen’S Inequality ◽  
Linear Functionals ◽  
Jensen's Inequality ◽  
Hadamard Inequality ◽  
Positive Linear Functionals ◽  
Main Inequality

The paper deals with the fundamental inequalities for convex functions in the bounded closed interval. The main inequality includes convex functions and positive linear functionals extending and refining the functional form of Jensen’s inequality. This inequality implies the Jensen, Fejér, and, thus, Hermite-Hadamard inequality, as well as their refinements.

scholarly journals Cauchy-type means for positive linear functionals

2011 ◽  
Vol 42 (4) ◽  
pp. 511-530
Author(s):  
M. Anwar ◽  
J. Pecaric ◽  
M. Rodi´c Lipanovi´c
Keyword(s):  
Jensen’S Inequality ◽  
Integral Form ◽  
Mean Value ◽  
Cauchy Type ◽  
Linear Functionals ◽  
Jensen's Inequality ◽  
Discrete Form ◽  
Mean Value Theorems ◽  
Positive Linear Functionals

Some mean-value theorems of the Cauchy type, which are connected with Jensen's inequality, are given in \cite{Mercer2} in discrete form and in \cite{PPSri} in integral form. Here we give the generalization of that result for positive linear functionals. Using that result, new means of Cauchy type for positive linear functionals are given. Monotonicity of these new means is also discussed.

scholarly journals SUPERADDITIVITY OF SOME FUNCTIONALS ASSOCIATED WITH JENSEN’S INEQUALITY FOR CONVEX FUNCTIONS ON LINEAR SPACES WITH APPLICATIONS

2010 ◽  
Vol 82 (1) ◽  
pp. 44-61 ◽  
Author(s):  
S. S. DRAGOMIR
Keyword(s):  
Information Theory ◽  
Convex Functions ◽  
Convex Sets ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Norm Inequalities ◽  
Linear Spaces ◽  
Normed Linear Spaces

AbstractSome new results related to Jensen’s celebrated inequality for convex functions defined on convex sets in linear spaces are given. Applications for norm inequalities in normed linear spaces and f-divergences in information theory are provided as well.

On Some Integral Inequalities Related to Hardy's

1977 ◽  
Vol 20 (3) ◽  
pp. 307-312 ◽  
Author(s):  
Christopher Olutunde Imoru
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Integral Inequalities ◽  
Hardy’S Inequality ◽  
Jensen's Inequality ◽  
Hardy's Inequality ◽  
Special Case

AbstractWe obtain mainly by using Jensen's inequality for convex functions an integral inequality, which contains as a special case Shun's generalization of Hardy's inequality.

INEQUALITIES OF JENSEN’S TYPE FOR POSITIVE LINEAR FUNCTIONALS ON HERMITIAN UNITAL BANACH -ALGEBRAS

2020 ◽  
Vol 102 (2) ◽  
pp. 308-318
Author(s):  
S. S. DRAGOMIR
Keyword(s):  
Convex Functions ◽  
Banach Algebras ◽  
General Setting ◽  
Linear Functionals ◽  
Positive Linear Functionals ◽  
Hermitian Unital

We establish inequalities of Jensen’s and Slater’s type in the general setting of a Hermitian unital Banach $\ast$-algebra, analytic convex functions and positive normalised linear functionals.

scholarly journals INEQUALITIES IN TERMS OF THE GÂTEAUX DERIVATIVES FOR CONVEX FUNCTIONS ON LINEAR SPACES WITH APPLICATIONS

2011 ◽  
Vol 83 (3) ◽  
pp. 500-517 ◽  
Author(s):  
S. S. DRAGOMIR
Keyword(s):  
Convex Functions ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Linear Spaces ◽  
Divergence Measures ◽  
Gateaux Derivatives ◽  
Gâteaux Derivatives

AbstractSome inequalities in terms of the Gâteaux derivatives related to Jensen’s inequality for convex functions defined on linear spaces are given. Applications for norms, mean f-deviations and f-divergence measures are provided as well.

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