Abstract
Under nearly additive and nearly convex functions we understand two modifications of additive functions and of convex functions: approximtely additive functions and approximtely convex functions, where the defining equation (5.2.1) resp. inequality (7.1.1) is satisfied only with some degree of accuracy, and almost additive functions and almost convex functions, where (5.2.1) resp. (5.3.1) is postulated only almost everywhere in the domain in question. (An interesting combination of both these conditions was considered by R. Ger [114].) Similar considerations will be carried out also for some other related classes of functions.
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© 2009 Birkhäuser Verlag AG
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(2009). Nearly Additive Functions and Nearly Convex Functions. In: Gilányi, A. (eds) An Introduction to the Theory of Functional Equations and Inequalities. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8749-5_17
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DOI: https://doi.org/10.1007/978-3-7643-8749-5_17
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8748-8
Online ISBN: 978-3-7643-8749-5
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