A GENERAL ITERATIVE ALGORITHM FOR THE SOLUTION OF VARIATIONAL INEQUALITIES FOR A NONEXPANSIVE SEMIGROUP IN BANACH SPACES - Sunthrayuth, P.; Kumam, P. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2011)
Let X be a uniformly convex and smooth Banach space which admits a weakly sequentially continuous duality mapping, C a nonempty bounded closed convex subset of X. Let S = T(s): 0 _ 0 < ∞ be a nonexpansive semigroup on C such that F(S) 6= and f : C → C is a contraction mapping with coefficient α (0, 1), A a strongly positive linear bounded operator with coefficient γ > 0. We prove that the sequences x_t and x_n are generated by the following iterative algorithms, respectively