scholarly journals A Refinement of Jensen's Inequality for a Class of Increasing and Concave Functions

2008 ◽  
Vol 2008 (1) ◽  
pp. 717614
Author(s):  
Ye Xia
Keyword(s):  
Jensen’S Inequality ◽  
Concave Functions ◽  
Jensen's Inequality

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 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.

On a global upper bound for Jensen's inequality

2009 ◽  
Vol 50 ◽  
Author(s):  
Julije Jaksetic ◽  
Bogdan Gavrea ◽  
Josip Pecaric
Keyword(s):  
Upper Bound ◽  
Jensen’S Inequality ◽  
Jensen's Inequality

scholarly journals New refinements of the discrete Jensen’s inequality generated by finite or infinite permutations

2019 ◽  
Vol 94 (6) ◽  
pp. 1109-1121
Author(s):  
László Horváth
Keyword(s):  
Banach Spaces ◽  
Jensen’S Inequality ◽  
Vector Spaces ◽  
Real Vector ◽  
Finite Sets ◽  
Jensen's Inequality

AbstractIn this paper some new refinements of the discrete Jensen’s inequality are obtained in real vector spaces. The idea comes from some former refinements determined by cyclic permutations. We essentially generalize and extend these results by using permutations of finite sets and bijections of the set of positive numbers. We get refinements of the discrete Jensen’s inequality for infinite convex combinations in Banach spaces. Similar results are rare. Finally, some applications are given on different topics.

Further sharpening of Jensen's inequality

Statistics ◽  
2021 ◽  
pp. 1-15
Author(s):  
Sang Kyu Lee ◽  
Jae Ho Chang ◽  
Hyoung-Moon Kim
Keyword(s):  
Jensen’S Inequality ◽  
Jensen's Inequality
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