Some KKM theorems in modular function spaces

Abstract

In this paper, a coincidence theorem is obtained which is generalization of Ky Fan's fixed point theorem in modular function spaces. A modular version of Fan's minimax inequality is proved. Moreover, some best approximation theorems are presented for multi-valued mappings.

Modular best proximity and equilibrium pairs in free generalized games

“…Next we shal show that φ i is ρ − L * -majorized in Y. By assumption (4), for each ∈ Y with i A i , φ i ( ) = P i ( ) is nonempty so that there exists a ρ − L * -majorant ψ i of φ i in Y by the assumption (3). For each ∈ Y with i ∈ A i , φ i ( ) = A i (f ) ∩ P i ( ).…”