Titlebook: An Introduction to the Theory of Functional Equations and Inequalities; Cauchy‘s Equation an Marek Kuczma,Attila Gilányi Textbook 2009Lates

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Subadditive FunctionsThe Jensen inequality (5.3.1) is not the natural counterpart of the Cauchy equation (5.2.1). The natural counterpart of the Cauchy equation would be the inequality ..

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Set Theorydamental role in the entire book. The mere existence of discontinuous additive functions and discontinuous convex functions depends on that axiom. Therefore the axiom of choice will equally be treated with the remaining axioms of the set theory and no special mention will be made whenever it is used

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Boundedness and Continuity of Convex Functions and Additive Functions? . is open and non-empty, and f is bounded above on T, then . is continuous in . Are there other sets . with this property? What are possibly weak conditions which assure the continuity of a convex function, or of an additive function? In this and in the next chapter we will deal with such question

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Properties of Hamel Bases.2.1 (cf., in particular, Corollary 4.2.1) asserts that there exist Hamel bases. More exactly (Lemma 4.2.1), for every set . ? . ? ?. such that . is linearly independent over ?, and . = ?., there exists a Hamel basis . of ?. such that . ? . ? . In particular, every set belonging to any of the classe

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alities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II give978-3-7643-8748-8978-3-7643-8749-5

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An Introduction to the Theory of Functional Equations and InequalitiesCauchy‘s Equation an

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Textbook 2009Latest editionut 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II give