Titlebook: Inequalities; Theorems, Techniques Zdravko Cvetkovski Book 2012 Springer-Verlag Berlin Heidelberg 2012 Cauchy-Schwarz inequality.H?lder’s i

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Zdravko CvetkovskiContains 485 problems on Algebra-Inequalities.Detailed solutions are given.Theoretical background and techniques for proving inequalities are provided.Ideal for participants of national and internatio

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Inequalities Between Means (with Two and Three Variables),In this section, we’ll first mention and give a proof of ., which are of particular importance for a full upgrade of the student in solving tasks in this area. It ought to be mentioned that in this section we will discuss the case that treats two or three variables, while the general case will be considered later in Chap.?..

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Geometric (Triangle) Inequalities,These inequalities in most cases have as variables the lengths of the sides of a given triangle; there are also inequalities in which appear other elements of the triangle, such as lengths of heights, lengths of medians, lengths of the bisectors, angles, etc.

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Inequalities Between Means (General Case),In Chap.?. we discussed . of two and three variables. In this section we will develop their generalization, i.e. we’ll present an analogous theorem for an arbitrary number of variables.

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,H?lder’s Inequality, Minkowski’s Inequality and Their Variants,In this chapter we’ll introduce two very useful inequalities with broad practical usage: . and .. We’ll also present few variants of these inequalities. For that purpose we will firstly introduce the following theorem.