- Title
- Criteria for epi/hypo convergence of finite-valued bifunctions
- Creator
- Diem, Huynh Thi Hong; Khanh, Phan Quoc
- Date
- 2015
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/89643
- Identifier
- vital:9282
- Identifier
-
https://doi.org/10.1007/s10013-015-0139-x
- Identifier
- ISSN:2305-221x
- Abstract
- Epi/hypo convergence of finite-valued bivariate functions defined on the product of two subsets, with some connections to lopsided convergence, is considered. Namely, we deal with three full characterizations of this convergence: by epi/hypo convergence of the corresponding proper bifunctions, by explicit formulae of the lower and upper members of the intervals of the limits, and by the bicontinuity of the partial Legendre-Fenchel transform (i.e., the (extended) epi/hypo convergence of bifunctions is characterized by the epi-convergence of their convex parents). We emphasize that epi/hypo limits are not unique and form an entire equivalence class. © 2015 Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.
- Publisher
- Springer Singapore
- Relation
- Vietnam Journal of Mathematics Vol. 43, no. 2 (2015), p. 439-458
- Rights
- Copyright © 2015 Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; Epi-convergence; Epi/hypo convergence; Equivalence class; Lopsided convergence; Partial Legendre-Fenchel transform; Partial skew conjugate
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