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.

Keywords:

• non-expansive mapping
• iterative process
• weak convergence
• strong convergence
• common fixed point

2000 MR Subject Classifications::

• 05C38
• 15A15