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.