Let S m, T m : C → C be asymptotically nonexpansive mappings, for every m ∈ { 1, 2, …, r }.
Moreover, by using our main result, we prove a strong convergence theorem for finding a common element of the set of fixed points of a finite family of η i -strictly pseudo-contractive mappings for every i = 1, 2, …, N in uniformly convex and 2-uniformly smooth Banach spaces.
Moreover, we prove a strong convergence theorem for finding a common element of the set of fixed points of a finite family of η i -strictly pseudo-contractive mappings for every i = 1, 2, …, N in uniformly convex and 2-uniformly smooth Banach spaces.
Let H be a real Hilbert space and let M i : H → 2 H be maximal monotone mappings for every i = 1, 2,... N. Let B i : H → H be a δ i - inverse strongly monotone mapping for every i = 1, 2,... N and { T i } i = 1 ∞ an infinite family of κ i - strictly pseudo-contractive mappings from H into itself.
Let H be a real Hilbert space, and let M i : H → 2 H be maximal monotone mappings for every i = 1, 2,..., N. Let B i : H → H be a δ i - inverse strongly monotone mapping for every i = 1, 2,..., N and { T i } i = 1 ∞ an infinite family of nonexpansive mappings from H into itself.
Then { x n } converges strongly to x 0 = P F u and ( x 0, y 0 ) is a solution of (1.3), where y 0 = P C ( I − λ 2 D 2 ) x 0. Proof First, we show that P C ( I − λ 1 D 1 ) and P C ( I − λ 2 D 2 ) are nonexpansive mappings for every λ 1 ∈ ( 0, 2 d 1 ), λ 2 ∈ ( 0, 2 d 2 ).
Let, be two set-valued mappings with for every, a single-valued mapping, and a subset of.
(ii)a semigroup of mappings if for every where.
Let T, S X X → X be given mappings satisfying for every pair ( x, y ) ∈ X × X.
Then and are said to be commuting mappings if for every such that and, we have.
Let T, S, R : X → X be given mappings, satisfying for every pair (x, y) ∈ X × X such that Rx and Ry are comparable: (2.1).
