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Vietnam Journal of Mathematics 40:2&3(2012) 165-180

 

Error Bounds for Vector-Valued Functions

on Metric Spaces

Ewa M. Bednarczuk1 and Alexander Y. Kruger2

1Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6,

Warszawa 01-447, Poland

2School of Science, Information Technology and Engineering,

Centre for Informatics and Applied Optimization, University of Ballarat,

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

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

Received November 6, 2011

Revised December 19, 2011

Abstract. In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivative-like objects–slopes–are introduced and a classification scheme of error bound criteria is presented.

2000 Mathematics Subject Classification. 49J52, 49J53, 58C06.

Keywords.  Variational analysis, error bounds, slope, vector variational principle.

 

 

 

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