Strong convergence theorems for fixed points of asymptotically pseudocontractive semi-groups

Let K be a nonempty closed convex and bounded subset of a real Banach space E. Let be a strongly continuous uniformly asymptotically regular and uniformly L-Lipschitzian semi-group of asymptotically pseudocontractive mappings from K into K. Then for a given u∈K there exists a sequence {y_n}∈K satisfying the equation y_n=(1−α_n)(T(t_n))ⁿy_n+α_nu for each , where α_n∈(0,1) and t_n>0 satisfy appropriate conditions. Suppose further that E is uniformly convex and has uniformly Gâteaux differentiable norm, under suitable conditions on the mappings T, the sequence {y_n} converges strongly to a fixed point of . Furthermore, an explicit sequence {x_n} generated from x₁∈K by x_n+1:=(1−λ_n)x_n+λ_n(T(t_n))ⁿx_n−λ_nθ_n(x_n−x₁) for all integers n?1, where {λ_n}, {θ_n} are positive real sequences satisfying appropriate conditions, converges strongly to a fixed point of .