Weak and strong convergence of a new scheme for two non-expansive mappings in Hilbert spaces

Abstract

In a real Hilbert space H, from an arbitrary initial point x 0 ∈ H, an iterative process is defined as follows: , , n ≥ 0, where , , (∀ x ∈ H), T, S : H → H are two non-expansive mapping with F(T) ∩ F(S) ≠ ∅ and f (resp. g) : H → H an η f (resp. η g )-strongly monotone and k f (resp. k g )-Lipschitzian mapping, {a n } ⊂ (0, 1), {b n } ⊂ (0, 1) and {λ n } ⊂ [0, 1), {β n } ⊂ [0, 1). Under some suitable conditions, several convergence results of the sequence {x n } are shown.