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Most people, when they think of mathematics, think first of numbers and equations-the number (x)=that number (y). But professional mathematicians, in dealing with quantities that can be ordered according to their size, often are more interested in unequal magnitudes that are equal. This book provides an introduction to the fascinating world of inequalities beginning with a systematic discussion of the relation 'greater than' and the meaning of 'absolute values' of numbers, and ending with descriptions of some unusual geometries. In the course of the book, the reader will encounter some of the more famous inequalities in mathematics. Starting with the basic order properties of real numbers, this book carries the reader through the classical inequalities of Cauchy, Minkowsky and Hörder with many variants and applications. The concluding chapter points the way to other metrics in the plane and the interrelations between geometry (convexity) and algebra (inequalities).

Inequalities (Mathematics)

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Hilbert-type integral inequalities, including the well known Hilbert's integral inequality published in 1908, are important in analysis and its applications. This well organized handbook covers the newest methods of weight functions and most important recent results of Hilbert-type integral inequalities and applications in three classes of normal spaces. It is clear and well written, suitable for researchers, mathematicians and advanced students who wish to increase their familiarity with different topics of modern and classical mathematical inequalities related to Real Analysis and Operator T

Inequalities (Mathematics)

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Inequalities (Mathematics) --- Processes, Infinite

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Anybody who liked their first geometry course (and some who did not) will enjoy the simply stated geometric problems about maximum and minimum lengths and areas in this book. Many of these already fascinated the Greeks, for example, the problem of enclosing the largest possible area by a fence of given length, and some were solved long ago; but others remain unsolved even today. Some of the solutions of the problems posed in this book, for example the problem of inscribing a triangle of smallest perimeter into a given triangle, were supplied by world famous mathematicians, other by high school students.

Geometry, Plane. --- Inequalities (Mathematics)

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Inequalities (Mathematics) --- Functions, Special.