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.

Autorentext

The author is a teacher of mathematics at Áprily Lajos high school in Brasov, Romania. He has written seven mathematical and five literary books. He is Editor in Chief of Octogon Mathematical Magazine. He has published more than 15.000 mathematical problems in 40 scientific journals, and more than 800 papers in journals all over the world.