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On general best proximity pairs and equilibrium pairs in free abstract economies. (English) Zbl 1136.91309
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 P. S. Srinivasan and 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 W. K. Kim and K. H. Lee [J. Math. Anal. Appl. 316, No. 2, 433–446 (2006; Zbl 1101.47040)] in several aspects.
91B50General equilibrium theory in economics
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47N10Applications of operator theory in optimization, convex analysis, programming, economics
54H25Fixed-point and coincidence theorems in topological spaces