and Applied Analysis 3 It is well known that, in an infinite dimensional Hilbert space, the normal Mann iterative algorithm has only weak convergence, in general, even for nonexpansive mappings. Hybrid projection algorithms are popular tool to prove strong convergence of iterative sequences without compactness assumptions. Recently, hybrid projection algorithms have received rapid developments;...

and Applied Analysis 3 xn ⇀ x ∈ X and ‖xn‖ → ‖x‖, then xn → x. It is known that if X is uniformly convex, then X has the Kadec-Klee property. The normalized duality mapping J from X to X∗ is defined by Jx { x∗ ∈ X∗ : 〈x, x∗〉 ‖x‖ ‖x∗‖2 } 2.3 for any x ∈ X. We list some properties of mapping J as follows. i If X is a smooth Banach space with Gâteaux differential norm , then J is singlevalued and ...

and Applied Analysis 3 F2 F t, xn, . . . , x0 W t, x0 − H t, xn, . . . , x0 , for every t ∈ Z, W,H are continuously differentiable in x0 and xn, . . . , x0, respectively. Moreover, there is a bounded set J ⊂ Z such that H t, xn, . . . , x0 ≥ 0; 2.2 F3 There is a constant μ > p such that 0 < μW t, x0 ≤ W ′ 2 t, x0 x0, ∀ t, x0 ∈ Z × R \ {0} ; 2.3 F4 H t, 0, . . . , 0 ≡ 0, and there is a constant ...