Communications of the
Korean Mathematical Society CKMS

Generalized Menger space introduced by the present authors is a generalization of Menger space as well as a probabilistic generalization of generalized metric space introduced by Branciari [Publ. Math. Debrecen {\bf 57} (2000), no.\,1-2, 31--37]. In this paper we prove a Kannan type fixed point theorem in generalized Menger spaces. We also support our result by an example.

Keywords: generalized Menger space, fixed point, Kannan type mapping, $\Psi$-function

MSC numbers: 47H10, 54H25