Existence of farthest points in Hilbert spaces

Let H be a real Hilbert space with the inner product <.,.> and the norm \|\cdot\|. In this paper, we introduce hybrid algorithms for generating cyclic, non-expansive mapping of H. Also, we discuss about necessary and sufficient conditions on subsets of Hilbert space to be remotal or uniquely remotal. Moreover, we give the basic concepts and theorems of farthest points of Bounded subsets of H. In the end, we will provide examples to illustrate our results.

Existence of farthest points in Hilbert spaces Keywords:

Best proximity point , Non-expansive mapping , F-property , Farthest point