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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.

Established by Vietnam Academy of Science and Technology & Vietnam Mathematical Society
Published by Springer since January 2013