Converse Edmundson-Lah-Ribarič inequalities and related results

Mikić, Rozarija (2017) Converse Edmundson-Lah-Ribarič inequalities and related results. Doctoral thesis, Faculty of Science > Department of Mathematics.

Language: Croatian

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A new class of functions that extends the class of 3-convex functions will be defined, and Levinson’s type generalization of the Edmundson-Lah-Ribarič inequality will be proved for those functions. Analogue generalizations of the Edmundson-Lah-Ribarič inequality for self-adjoint operators in Hilbert space and for their scalar product will be proved. Next, inequalities of Jensen and Edmundson-Lah-Ribarič for positive linear functionals will be studied. New inequalities of difference type, as well as their refinements and improvements, will be obtained. These results will be applied to generalized means and some famous inequalities (the ones of Hölder, Hermite-Hadamard, Giaccardi and Petrović). Further, converses of the Jensen and Edmundson-Lah-Ribarič operator inequalities and their refinements and improvements will be obtained. General results will be applied to quasi-arithmetic operator means and to potential operator means. Finally, converses of Ando’s and Davis-Choi’s inequality, as well as the Edmundson-Lah-Ribarič and its converse of difference type for positive unital mappings, will be studied. Ratio and difference type converses will be proved for a special type of solidarities which includes connections, and for relative operator entropy.

Item Type: Thesis (Doctoral thesis)
Keywords: Jensen’s inequality, the Edmundson-Lah-Ribarič inequality, convexity, positive linear functionals, self-adjoint operators, unital linear mappings, solidarity, connections, operator entropy, Levinson’s inequality, scalar product
Supervisor: Pečarić, Josip
Date: 2017
Number of Pages: 106
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 24 May 2017 11:27
Last Modified: 24 May 2017 11:27

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