On Proximal Mappings with Young Functions in Uniformly Convex Banach Spaces

被引:0
作者
Bacak, Miroslav [1 ]
Kohlenbach, Ulrich [2 ]
机构
[1] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany
[2] Tech Univ Darmstadt, Dept Math, Schlossgartenstr 7, D-64289 Darmstadt, Germany
关键词
Convex function; duality mapping; modulus of uniform convexity; proximal mapping; uniformly convex Banach space; uniformly convex function; Young function; ANALYSE FONCTIONNELLE; REGULARIZATION; APPROXIMATION; INEQUALITIES; CONVERGENCE; SMOOTHNESS; ENVELOPES; OPERATORS; SETS;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
It is well known in convex analysis that proximal mappings on Hilbert spaces are 1-Lipschitz. In the present paper we show that proximal mappings on uniformly convex Banach spaces are uniformly continuous on bounded sets. Moreover, we introduce a new general proximal mapping whose regularization term is given as a composition of a Young function and the norm, and formulate our results at this level of generality. It is our aim to obtain the corresponding modulus of uniform continuity explicitly in terms of a modulus of uniform convexity of the norm and of moduli witnessing properties of the Young function. We also derive several quantitative results on uniform convexity, which may be of interest on their own.
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页码:1291 / 1318
页数:28
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