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Variational Relations in Abstract Convex Spaces -by Sehie Park

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Abstract: Luc [1] initiated the study of variational relations, which is a unifying approach to various models of equilibrium theory and variational inclusions. There, a simple condition was established for the existence of solutions of variational relations and was applied to a number of variational problems. In the present article, certain results in [1] are generalized by reflecting recent development of the KKM theory on abstract convex spaces.

Keywords: Variational relations, Equilibria, Variational inequalities, Abstract convex space, (Partial) KKM space and Fixed point.

DOI: https://doi.org/10.30697/rfpta-2018-014

How to cite this article: Sehie Park, Variational Relations in Abstract Convex Spaces, Results in Fixed Point Theory and Applications, vol. 2018, Article ID 2018014, 08 pages, 2018.

Copyright © 2018 SUMA Publishing Group., This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.