Topics in Contemporary Mathematical Analysis and Applications

7 On Some Important Inequalities

Zlatko Pavić

University of Osijek

CONTENTS

7.1     Concepts of Affinity and Convexity

7.1.1     Affine and Convex Sets and Functions

7.1.2     Effect of Affine and Convex Combinations in ℝⁿ

7.1.3     Coefficients of Affine and Convex Combinations

7.1.4     Support and Secant Hyperplanes

7.2     The Jensen Inequality

7.2.1     Discrete and Integral Forms of the Jensen Inequality

7.2.2     Generalizations of the Jensen Inequality

7.3     The Hermite-Hadamard Inequality

7.3.1     The Classic Form of the Hermite-Hadamard Inequality

7.3.2     Generalizations of the Hermite-Hadamard Inequality

7.4     The Rogers-Hölder Inequality

7.4.1     Integral and Discrete Forms of the Rogers-Hölder Inequality

7.4.2     Generalizations ...