OPERATOR QUASILINEARITY OF SOME FUNCTIONALS ASSOCIATED WITH DAVIS–CHOI–JENSEN’S INEQUALITY FOR POSITIVE MAPS

2016 ◽  
Vol 95 (2) ◽  
pp. 322-332
Author(s):  
S. S. DRAGOMIR
Keyword(s):  
Power Function ◽  
Jensen’S Inequality ◽  
Concave Functions ◽  
Jensen's Inequality ◽  
Positive Maps ◽  
Operator Convex

In this paper we establish operator quasilinearity properties of some functionals associated with Davis–Choi–Jensen’s inequality for positive maps and operator convex or concave functions. Applications for the power function and the logarithm are provided.

scholarly journals Some Hermite-Hadamard type inequalities for operator convex functions and positive maps

2019 ◽  
Vol 7 (1) ◽  
pp. 38-51 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Power Function ◽  
Convex Functions ◽  
Positive Maps ◽  
Operator Convex ◽  
Operator Convex Functions

Abstract In this paper we establish some inequalities of Hermite-Hadamard type for operator convex functions and positive maps. Applications for power function and logarithm are also provided.

Cyclic Refinements of the Different Versions of Operator Jensen's Inequality

2016 ◽  
Vol 31 ◽  
pp. 125-133 ◽  
Author(s):  
Laszlo Horvath ◽  
Khuram Khan ◽  
Josip Pecaric
Keyword(s):  
Convex Functions ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Norm Inequalities ◽  
Power Means ◽  
Operator Convex ◽  
Operator Convex Functions

Refinements of the operator Jensen's inequality for convex and operator convex functions are given by using cyclic refinements of the discrete Jensen's inequality. Similar refinements are fairly rare in the literature. Some applications of the results to norm inequalities, the Holder McCarthy inequality and generalized weighted power means for operators are presented.

scholarly journals Reversing Jensen’s Inequality for Information-Theoretic Analyses

Information ◽  
2022 ◽  
Vol 13 (1) ◽  
pp. 39
Author(s):  
Neri Merhav
Keyword(s):  
Information Theory ◽  
Jensen’S Inequality ◽  
Jensen Inequality ◽  
Concave Functions ◽  
Jensen's Inequality ◽  
Information Theoretic ◽  
Main Ideas

In this work, we propose both an improvement and extensions of a reverse Jensen inequality due to Wunder et al. (2021). The new proposed inequalities are fairly tight and reasonably easy to use in a wide variety of situations, as demonstrated in several application examples that are relevant to information theory. Moreover, the main ideas behind the derivations turn out to be applicable to generate bounds to expectations of multivariate convex/concave functions, as well as functions that are not necessarily convex or concave.

Some Generalizations of Jensen's Inequality

2020 ◽  
Author(s):  
Slavko Simic ◽  
Bandar Almohsen
Keyword(s):  
Target Function ◽  
Jensen’S Inequality ◽  
Convexity Property ◽  
Concave Functions ◽  
Jensen's Inequality ◽  
Differentiable Functions ◽  
Probability And Statistics

In this article, we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They represent a refinement of these inequalities in the case of convex/concave functions with numerous applications in Theory of Means and Probability and Statistics.

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