- Title
- Borwein-Preiss variational principle revisited
- Creator
- Kruger, Alexander; Plubtieng, Somyot; Seangwattana, Thidaporn
- Date
- 2016
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100317
- Identifier
- vital:10517
- Identifier
-
https://doi.org/10.1016/j.jmaa.2015.11.009
- Identifier
- ISSN:0022-247X
- Abstract
- In this article, we refine and slightly strengthen the metric space version of the Borwein-Preiss variational principle due to Li and Shi (2000) [12], clarify the assumptions and conclusions of their Theorem 1 as well as Theorem 2.5.2 in Borwein and Zhu (2005) [4] and streamline the proofs. Our main result, Theorem 3 is formulated in the metric space setting. When reduced to Banach spaces (Corollary 9), it extends and strengthens the smooth variational principle established in Borwein and Preiss (1987) [3] along several directions. (C) 2015 Elsevier Inc. All rights reserved.
- Publisher
- Elsevier Ltd
- Relation
- Journal of Mathematical Analysis and Applications Vol. 435, no. 2 (2016), p. 1183-1193; http://purl.org/au-research/grants/arc/DP110102011
- Rights
- Copyright © 2015 Elsevier Inc. All rights reserved.
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; 0102 Applied Mathematics; 0906 Electrical and Electronic Engineering; Borwein-Preiss variational principle; Smooth variational principle; Gauge-type function; Perturbation
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