scholarly journals A new refinement of Jensen’s inequality in linear spaces with applications

2010 ◽  
Vol 52 (9-10) ◽  
pp. 1497-1505 ◽  
Author(s):  
S.S. Dragomir
Keyword(s):  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Linear Spaces

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.

scholarly journals Bounds for the normalised Jensen functional

2006 ◽  
Vol 74 (3) ◽  
pp. 471-478 ◽  
Author(s):  
Sever S. Dragomir
Keyword(s):  
Convex Functions ◽  
Jensen’S Inequality ◽  
Normed Spaces ◽  
Jensen's Inequality ◽  
Linear Spaces ◽  
Leibler Divergence ◽  
Jensen Functional ◽  
New Inequalities

New inequalities for the general case of convex functions defined on linear spaces which improve the famous Jensen's inequality are established. Particular instances in the case of normed spaces and for complex and real n-tuples are given. Refinements of Shannon's inequality and the positivity of Kullback-Leibler divergence are obtained.

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 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.

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