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Zbl 1136.91309
Kim, Won Kyu; Kum, Sangho; Lee, Kyoung Hee
On general best proximity pairs and equilibrium pairs in free abstract economies. (English)
[J] Nonlinear Anal., Theory Methods Appl. 68, No. 8, A, 2216-2227 (2008). ISSN 0362-546X

Summary: Using Lassonde's fixed point theorem for Kakutani factorizable multifunctions and Park's fixed point theorem for acyclic factorizable multifunctions, we will prove new existence theorems for general best proximity pairs and equilibrium pairs for free abstract economies, which generalize the previous best proximity theorems and equilibrium existence theorems due to {\it P. S. Srinivasan} and {\it P. Veeramani} [Abstr. Appl. Anal. 2003, No. 1, 33--47 (2003; Zbl 1023.47035); Fixed Point Theory Appl. 2004, No. 1, 21--29 (2004; Zbl 1091.47060)], and {\it W. K. Kim} and {\it K. H. Lee} [J. Math. Anal. Appl. 316, No. 2, 433--446 (2006; Zbl 1101.47040)] in several aspects.

MSC 2000:: *91B50 Equilibrium in economics
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47N10 Appl. of operator theory in optimization, math. programming, etc.
54H25 Fixed-point theorems in topological spaces

Keywords: best proximity pairs; equilibrium pairs; free abstract economy; Kakutani factorizable multifunction; fixed point; acyclic value

Citations: Zbl 1023.47035; Zbl 1091.47060; Zbl 1101.47040

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