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1	Nejednakosti Jensena i Čebiševa za intervalno-vrednosne funkcije / Jensen and Chebyshev inequalities for interval-valued functions Medić Slavica 25 April 2014 (has links) <p>Integralne nejednakosti Jensena i Čebiševa<br />uopštene su za integrale bazirane na neaditivnim<br />merama. Prvo uopštenje dokazano je za<br />pseudo-integral skupovno-vrednosne  funkcije, a<br />drugo za pseudo-integral realno-vrednosne funkcije<br />u odnosu na intervalno-vrednosnu -meru.<br />Dokazana je i uopštena nejednakost Čebiševa<br />za pseudo-integral realno-vrednosne  funkcije i<br />njena dva intervalno-vrednosna oblika. Nejednakost<br />Jensena je primenjena u principu premije, a<br />nejednakost Čebiševa na procenu verovatnoće.</p> / <p>Integral inequalities of Jensen and Chebyshev type are<br />generalized for integrals based on nonadditive measures.<br />The first generalization is proven for the pseudointegral<br />of a set valued function and the second one<br />for the pseudo-integral of a real-valued function with<br />respect to the interval-valued -measure. Generalized<br />Chebyshev inequality for the pseudo-integral of a realvalued<br />function and its two interval-valued forms are<br />proven. Jensen inequality is applied in the premium<br />principle and Chebyshev inequality is applied to the<br />probability estimation.</p>
2	Jensen Inequality, Muirhead Inequality and Majorization Inequality Chen, Bo-Yu 06 July 2010 (has links) Chapter 1 introduces Jensen Inequality and its geometric interpretation. Some useful criteria for checking the convexity of functions are discussed. Many applications in various fields are also included. Chapter 2 deals with Schur Inequality, which can easily solve some problems involved symmetric inequality in three variables. The relationship between Schur Inequality and the roots and the coefficients of a cubic equation is also investigated. Chapter 3 presents Muirhead Inequality which is derived from the concept of majorization. It generalizes the inequality of arithmetic and geometric means. The equivalence of majorization and Muirhead¡¦s condition is illustrated. Two useful tricks for applying Muirhead Inequality are provided. Chapter 4 handles Majorization Inequality which involves Majorization and Schur convexity, two of the most productive concepts in the theory of inequalities. Its applications in elementary symmetric functions, sample variance, entropy and birthday problem are considered. system of distinct representatives Three Chord Lemma Birkhoff Theorem convex function concave function convex hull double stochastic matrix Jensen Inequality Lorenz Curve Majorization Inequality majorization Muirhead Inequality Muirhead condition Schur concave function Schur Criterion Schur convex function Schur Inequality supporting line Supporting Line Inequality

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Nejednakosti Jensena i Čebiševa za intervalno-vrednosne funkcije / Jensen and Chebyshev inequalities for interval-valued functions

Jensen Inequality, Muirhead Inequality and Majorization Inequality