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.