caa a22 4500 388092149 CHVBK 20180307125254.0 cr unu---uuuuu 161130e199908 xx s 000 0 eng 10.1017/S0004972700033372 doi S0004972700033372 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700033372 Smooth variational principles in Radon-Nikodým spaces [Elektronische Daten] We prove that if f is a real valued lower semicontinuous function on a Banach space X, for which there exist a > 0 and b ∈ ℝ such that f(x) ≥ 2a∥x∥ + b, x ∈ X, and if X has the Radon-Nikody´m property, then for every Ε > 0 there exists a real function φ X such that φ is Fréchet differentiable, ∥φ∥∞ < Ε, ∥φ′∥∞ < Ε, φ′ is weakly continuous and f + φ attains a minimum on X. In addition, if we assume that the norm in X is β-smooth, we can take the function φ = g1 + g2 where g1 is radial and β-smooth, g2 is Fréchet differentiable, ∥g1∥∞ < Ε, ∥g2∥∞ < Ε, ∥g′1∥∞ < Ε, ∥g′1∥∞ < Ε, g′2 is weakly continuous and f + g1 + g2 attains a minimum on X. Copyright © Australian Mathematical Society 1999 Deville Robert Université Bordeaux 1 Faculté des Sciences Laboratoire de Mathématiques pures 351 cours de la Libération 33400 Talence France Maaden Abdelhakim Université Cadi-Ayyad Faculté des Sciences et Techniques Departement de Mathematiques B.P. 523 Béni-Mellal Maroc Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 109-118 0004-9727 60:1<109 1999 60 BAZ https://doi.org/10.1017/S0004972700033372 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700033372 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Deville Robert Université Bordeaux 1 Faculté des Sciences Laboratoire de Mathématiques pures 351 cours de la Libération 33400 Talence France NATIONALLICENCE 700 1- Maaden Abdelhakim Université Cadi-Ayyad Faculté des Sciences et Techniques Departement de Mathematiques B.P. 523 Béni-Mellal Maroc NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 109-118 0004-9727 60:1<109 1999 60 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge