A fixed point theorem for asymptotically nonexpansive mappings

Let K be a subset of a Banach space X . A mapping F : K → K F:K \to K is said to be asymptotically nonexpansive if there exists a sequence { k i } \{ {k_i}\} of real numbers with k i → 1 {k_i} \to 1 as i → ∞ i \to \infty such that ‖ F i x − F i y ‖ ≦ k i ‖ x − y ‖ , x , y ∈ K \left \| {{F^i}x - {F^i... View More