On Kannan maps

  title={On Kannan maps},
  author={Chi Song Wong},
Let K be a (nonempty) weakly compact convex subset of a Banach space B. Let T be a self map on K such that for all x, y in K, IT(x) T(y) < (|lx T(x)l + IYT(y)ll)/2. It is proved without the continuity of T and Zorn's lemma that T has a fixed point if and only if inflx T(x)ll: x E Ki =0. A characterization of the existence of fixed points for such T is obtained in terms of close-to-normal structure. As consequences, the following results are obtained: (i) T has a unique fixed point if B is… CONTINUE READING