New Inequalities based on convexity
2D-convexity and its appilactions
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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 inte...
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.
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