In this paper, we prove the demiclosed principle for total asymptotically nonexpansive nonself mappings in hyperbolic spaces. Then we obtain convergence theorems of the mixed Agarwal-O'Regan-Sahu type iteration for total asymptotically nonexpansive nonself mappings. Our results extend some results in the literature. MSC: 47H09; 49M05

Abstract. The existence of homoclinic orbits is obtained for a class of the second order Hamiltonian systemsü(t) − L(t)u(t) + ∇W (t,u(t)) = 0, ∀t ∈ R , by the mountain pass theorem, where W (t,x) needs not to satisfy the global (AR) condition. Mathematics subject classification

In this paper, we prove some -convergence theorems in a hyperbolic space. A mixed Agarwal-O'Regan-Sahu type iterative scheme for approximating a common fixed point of total asymptotically nonexpansive mappings is constructed. Our results extend some results in the literature. MSC: 47H09; 49M05

Abstract. The existence of homoclinic orbits is obtained for a class of the second order Hamiltonian systemsü(t) − L(t)u(t) + ∇W (t,u(t)) = 0, ∀t ∈ R , by the mountain pass theorem, where W (t,x) needs not to satisfy the global (AR) condition.

Under some local superquadratic conditions on