we introduce a new one-step iteration process to approximate common fixed points of twononexpansive mappings in banach spaces and prove weak convergence of the iterative sequence using (i)opial’s condition and (ii) kadec-klee property. strong convergence theorems are also established in banachspaces and uniformly convex banach spaces under the so-called condition ( a ), which is weaker thancom...

in this paper we derive convergence theorems for an -nonexpansive mappingof a nonempty closed and convex subset of a complete cat(0) space for sp-iterative process and thianwan's iterative process.

and Applied Analysis 3 where S1 is a nonexpansive mapping. They proved that the sequence {xn} defined by 1.6 strongly converge to x∗ ∈ F S1 ⋂ VI C, T , if the coefficient αn, λn satisfy the following conditions:

Let H be a real Hilbert space, C a nonempty closed convex subset of H , and T : C → C a mapping. Recall that T is nonexpansive if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. A point x ∈ C is called a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T , that is, F(T) = {x ∈ C : Tx = x}. Recall that a self-mapping f : C → C is a contraction on C, if there exists a constant α∈ (0...

Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, F {T h : h ≥ 0} a generalized asymptotically nonexpansive self-mapping semigroup of K, and f : K → K a fixed contractive mapping with contractive coefficient β ∈ 0, 1 . We prove that the following implicit and modified implicit viscosity iterative schemes {xn}...

For the approximation of fixed points of a nonexpansive operator T in a uniformly convex Banach space E the convergence of the Mann-Toeplitz iteration x„+1 = a„T(x„) + (1 a„)xñ is studied. Strong convergence is established for a special class of operators T. Via regularization this result can be used for general nonexpansive operators, if E possesses a weakly sequentially continuous duality map...

Let C be a nonempty, closed, and convex subset of a real Hilbert space H . Denote the metric projection from x ∈ H onto C by PCx. Let T : C → C be a nonexpansive mapping on C, that is, T : C → C and ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. We use F T to denote the set of fixed points of T , that is, F T {x ∈ C : x Tx}. Let {T s : s > 0} be a nonexpansive semigroup on a closed convex subset C, tha...

Let C be a closed convex subset of a Banach space E. A mapping T on C is called a nonexpansive mapping if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F(T) the set of fixed points of T . Kirk [17] proved that F(T) is nonempty in the case that C is weakly compact and has normal structure. See also [2, 3, 5, 6, 11] and others. Convergence theorems to fixed points are also proved by many author...

In this paper, we introduce a new iterative scheme for finding the common element of the set of common fixed points of infinitely many nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of a general system of variational inequalities for inverse-strongly monotone mappings in Hilbert spaces. We prove that the sequence converges strongly to a common ele...

In this paper, we study a fixed-point problem with set-valued mapping by using an algorithm based on unions of nonexpansive mappings. We show that approximate solution is reached after finite number iterations in the presence computational errors. This result extension results known literature.