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Vietnam Journal of Mathematics 40:2&3(2012) 355-369

 

Slopes of Multifunctions and Extensions of Metric Regularity

Huynh Van Ngai1, Alexander Y. Kruger2 and Michel Théra3

1Department of Mathematics, Quy Nhon University, 170 An Duong Vuong,

Quy Nhon, Vietnam

2Centre for Informatics and Applied Optimization, School of Science,

Information Technology and Engineering, University of Ballarat,

P. O. B. 663, Ballarat, Vic, 3350, Australia

3Laboratoire XLIM, UMR-CNRS 6172, Université de Limoges, Limoges, France

Dedicated to Professor Phan Quoc Khanh on the occasion of his 65th birthday

Received January 24, 2012

Revised April 24, 2012

Abstract. This article aims to demonstrate how the definitions of slopes can be extended to multi-valued mappings between metric spaces and applied for characterizing metric regularity. Several kinds of local and nonlocal slopes are defined and several metric regularity properties for set-valued mappings between metric spaces are investigated.

2000 Mathematics Subject Classification. 49J52, 49J53, 58C06, 47H04, 54C60.

Keywords. Variational analysis, error bounds, slope, multifunction, metric regularity.

 

 

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