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作者:Daniel Azagra
来源:[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2020, Vol.486 (2)
摘要:Abstract(#br)We make some remarks on the global shape of continuous convex functions defined on a Banach space Z . For instance we show that if Z is separable then for every continuous convex function f : Z → R there exists a unique closed linear subspace Y f of Z such that,...
作者:Marek Żołdak
来源:[J].Aequationes mathematicae(IF 0.422), 2017, Vol.91 (6), pp.1093-1101
摘要:Let \((G,+)\) be an Abelian topological group, which is also a \(T_{0}\) -space and a Baire space simultaneously, D be an open connected subset of G and \(\alpha : D-D \rightarrow {\mathbb R}\) be a function continuous at zero and such that \(\alpha (0)=0\) . We show that if \((f...
作者:Daniel Azagra , Carlos Mudarra
来源:[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2017, Vol.446 (2), pp.1167-1182
摘要:Abstract(#br)Let H be a Hilbert space, E ⊂ H be an arbitrary subset and f : E → R , G : E → H be two functions. We give a necessary and sufficient condition on the pair ( f , G ) for the existence of a convex function F ∈ C 1 , 1 ( H ) such that F = f and ∇ F = G on ...
作者:Shaoqiang Shang
来源:[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2019, Vol.478 (2), pp.526-538
摘要:Abstract(#br)This article is devoted to smooth approximation of convex functions on Banach spaces with smooth norm. We prove that if X ⁎ is a smooth space and f is a w ⁎ -lower semicontinuous Lipschitzian convex function on X ⁎ , then there exist two w ⁎ -lower semicont...
作者:Jakub Rondoš , Jiří Spurný
来源:[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2020, Vol.484 (2)
摘要:Abstract(#br)Let X be a compact convex set and let ext X stand for the set of extreme points of X . Let f : X → R be a bounded convex function with the point of continuity property. The first main result shows that f ≤ 0 on X provided f ≤ 0 on ext X . As a byproduct of ou...
作者:Lixin Cheng , Yingbin Ruan , Yanmei Teng
来源:[J].Journal of Approximation Theory(IF 0.755), 2002, Vol.116 (1), pp.126-140
摘要:Abstract(#br)This paper shows that every w *-lower semicontinuous Lipschitzian convex function on the dual of a locally uniformly convexifiable Banach space, in particular, the dual of a separable Banach space, can be uniformly approximated by a generically Fréchet differen...
作者:Ming Li , Toshiyuki Sugawa
来源:[J].Computational Methods and Function Theory(IF 0.5), 2017, Vol.17 (2), pp.179-193
摘要:In this note, we investigate the supremum and the infimum of the functional \(|a_{n+1}|-|a_{n}|\) for functions, convex and analytic on the unit disk, of the form \(f(z)=z+a_2z^2+a_3z^3+\cdots .\) We also consider the related problem of maximizing the functional \(|a_{n+1}-a_{n}|...
作者:Paweł A. Kluza
来源:[J].Physica A: Statistical Mechanics and its Applications(IF 1.676), 2019
摘要:Abstract(#br)In this paper, Rényi type f -divergences like Jensen-Rényi and Jeffreys-Rényi are studied for convex functions. Some comparison theorems for two divergences are provided. The obtained results imply for introduced divergences some new inequalities corresponding...
作者:Dušan Pokorný , Martin Rmoutil
来源:[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2014, Vol.415 (2), pp.803-815
摘要:Abstract(#br)In the present article we provide a sufficient condition for a closed set F ∈ R d to have the following property which we call c -removability: Whenever a continuous function f : R d → R is locally convex on the complement of F , it is convex on the whole R d . ...
作者:Jaspal Singh Aujla , Fernando C. Silva
来源:[J].Linear Algebra and Its Applications(IF 0.968), 2003, Vol.369, pp.217-233
摘要:Abstract(#br)Let f be a convex function defined on an interval I , 0⩽ α ⩽1 and A , B n × n complex Hermitian matrices with spectrum in I . We prove that the eigenvalues of f ( αA +(1− α ) B ) are weakly majorized by the eigenvalues of αf ( A )+(1− α ) f ( B ). Fur...

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