Feng-Liu and Kikkawa-Suzuki contractions on sets with a cyclical representation and applications to best proximity point theory

In this paper we will prove fixed point theorems for two classes of cyclic multi-valued contractions: Feng-Liu type contractions and Kikkawa-Suzuki type contractions. An application to the best proximity points problem is given. Some stability properties for the fixed point inclusion, such as Ulam-Hyers stability, well-posedness in the sense of Reich and Zaslavski, and data dependence of the fixed point set are also proved. Finally, an extension of the Feng-Liu and Kikkawa-Suzuki approaches is given and a fixed point result for a Feng-Liu-Kikkawa-Suzuki contraction is obtained.