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Vietnam Journal of Mathematics 40:2&3(2012)
165-180
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Error Bounds for Vector-Valued Functions
on Metric Spaces
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Ewa M. Bednarczuk1 and
Alexander Y. Kruger2
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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
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Dedicated to Professor
Phan Quoc Khanh on the occasion of his 65th birthday
Received November 6,
2011
Revised December 19,
2011
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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.
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2000 Mathematics
Subject Classification. 49J52, 49J53, 58C06.
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Keywords. Variational analysis, error bounds,
slope, vector variational principle.
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Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
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