and Applied Analysis 3 where K and Q are nonempty closed convex subsets of the infinite-dimension real Hilbert spaces H1 and H2, respectively, and A is bounded linear mapping from H1 to H2. Equation 1.9 models many applied problems arising from image reconstructions and learning theory see, e.g., 4 . Someworks on the finite dimensional setting with relevant projectionmethods for solving image r...

and Applied Analysis 3 Definition 1.1. A one-parameter family mapping S {T t : t ∈ R } from C into itself is said to be a nonexpansive semigroup on C if it satisfies the following conditions: i T 0 x x for all x ∈ C, ii T s t T s ◦ T t for all s, t ∈ R , iii for each x ∈ C the mapping t → T t x is continuous, iv ‖T t x − T t y‖ ≤ ‖x − y‖ for all x, y ∈ C and t ∈ R . Remark 1.2. We denote by F S...

and Applied Analysis 3 the equilibrium problems, we also have the problems of finding the fixed points of the nonlinear mappings, which is the subject of current interest in functional analysis. It is natural to construct a unified approach for these problems. In this direction, several authors have introduced some iterative schemes for finding a common element of the set of solutions of the eq...