On general best proximity pairs and equilibrium pairs in free abstract economies Original Research Article

In this paper, 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 Srinivasan and Veeramani [P.S. Srinivasan, P. Veeramani, On best approximation pair theorems and fixed point theorems, Abstr. Appl. Anal. 2003 (1) (2003) 33–47; P.S. Srinivasan, P. Veeramani, On existence of equilibrium pair for constrained generalized games, Fixed Point Theory Appl. 2004 (1) (2004) 21–29], and Kim and Lee [W.K. Kim, K.H. Lee, Existence of best proximity pairs and equilibrium pairs, J. Math. Anal. Appl. 316 (2006) 433–446] in several aspects.