New Inequalities Based on Convexity

In this book I present new inequalities based on convexity. The first chapter is devoted to the Popoviciu's inequality for functions of several variables. The notion of 2D-convex function is introduced and several results are presented like the 2D analogue of Jensen's inequality the version of Hermite-Hadamard type inequality the analogue of midpoint convexity convolution of 2D-convex functions and the nice proof of the classical Popoviciu's inequality based on the mathematical induction. In the second chapter I studied in seven sections the Hilbert-type inequalities Hardy-Hilbert integral inequality etc. In the third chapter I present in six sections: the Hermite-Hadamard integral inequality the Simpson-type Newton-type and Gauss-type inequalities. In the chapter four I discuss the Schur convexity of generalized Heronian means involving two parameters. Chapter five has nine sections and studies the Brunn-Minkowski inequality.