Notes on weak and strong convergence theorems for a finite family of asymptotically strict pseudo-contractive mappings in the intermediate sense

摘要

Let H be a real Hilbert space with norm || • || and C be a nonempty closed convex subset of H. Let T : C →C be a mapping. Recall the following concepts.(i) T is asymptotically nonexpansive with a sequence {k_n} [1] if k_n ∈[1, +00) with lim_(n→∞) k_n = 1 are such that ||T~nx-T~ny|| ≤K_nl|x-y||, ∨_x, y ∈C and n ∈N.(ii) T is called asymptotically nonexpansive in the intermediate sense [2] if T is uniformly continuous and lim sup sup (||T~nx - T~ny|| - ||x - y||) ≤ 0.