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Acta Applicandae Mathematicae 24: (1991). 195 Book Reviews D. G. de Figueiredo: Lectures on The Ekeland Variational Principle with Applications and Detours, Tata Institute of Fundamental Research, Bombay, Lectures on Mathematics and Physics-Mathematics 81, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1989, 96 pp., Softcover DM20,-, ISBN 3-540-51179-2. This monograph is devoted to explaining the Ekeland variational principle (EVP) and its applications. Since its appearance in 1972, this principle has found many applications in different fields of analysis. The most general version of the EVP presented in these notes is the following: Let (X, d) be a complete metric space. Let O: X ~ R w { +~} be a lower semicontinuous function which is bounded below. Let e > 0 and ft~X be given such that O(fi) ~< infx • + e/2. Then, #iven 2 > 0, there exists u~ ~ X such that O(uz) ~< O(fi), d(u~, ~) <~ 2, @(uz) < O(u) + -2 d(u, u~t) , Vu ~ u;~. In Chapter 1, the notions of lower semicontinuity (1.s.c.) and sequential lower semicontinuity are introduced and relations between them are studied. The well- known theorem about the existence of the minimizing point of a 1.s.c. functional over
Acta Applicandae Mathematicae – Springer Journals
Published: May 1, 2004
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