and Applied Analysis 3 Let C be a nonempty closed convex subset of a real Hilbert space H. Recall that a mapping A : C → H is called α-inverse strongly monotone if there exists a positive real number α such that 〈Ax − Ay, x − y〉 ≥ α‖Ax −Ay‖, for all x, y ∈ C. It is clear that any αinverse strongly monotone mapping is monotone and 1/α-Lipschitz continuous. Let f : C → H be a ρ-contraction; that ...

We introduce an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse stronglymonotonemappings, the set of solutions of an equilibrium problem, and the set of fixed points of a nonexpansive mapping. We obtain a strong convergence theorem for the sequences generated...

In this paper, first, we introduce the condition (BP) which is weaker than the completely continuous mapping in Banach spaces. Second, we consider a simple iteration and prove some strong convergence theorems of the proposed iteration for an asymptotically nonexpansive nonself-mapping with the condition (BP). Finally, we give two examples to illustrate the main result in this paper. Our results...

We denote by F(T) the set of fixed points of T. Numerous problems in physics, optimization, and economics reduce to find a solution of the equilibrium problem. Some methods have been proposed to solve the equilibrium problem in a Hilbert spaces; see, for instance, Blum and Oettli [1], Combettes and Hirstoaga [2], and Moudafi [3]. Recently, Tada and Takahashi [4, 5] and S. Takahashi and W. Takah...

and Applied Analysis 3 Moreover, PC is characterized by the following properties: 〈 x − PCx, y − PCx 〉 ≤ 0, ∥ ∥x − y∥∥2 ≥ ‖x − PCx‖ ∥ ∥y − PCx ∥ ∥ 2 , 2.4 for all x ∈ H and y ∈ C. We also need other sorts of nonlinear operators which are introduced below. Let T : H → H be a nonlinear operator. a T is nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖ for all x, y ∈ H. b T is firmly nonexpansive if 2T − I is n...

Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equation du(t)/dt + Au(t)+ G(u)(t) f(t), where A is a maximal monotone operator in a nilbert space H,f E LI(0,:H) and G:C([O,c):D(A))LI(O,c:H)is a given mapping.

Let C be a bounded closed convex subset of a uniformly convex Banach space X and let = = {T (t) : t ∈ G} be a commutative semigroup of asymptotically nonexpansive in the intermediate mapping from C into itself. In this paper, we provide the strong mean ergodic convergence theorem for the almost-orbit of =.

In this paper, we consider the problem of finding a common fixed point of a nonexpansive mapping and a λ-strict pseudocontraction based on a general iterative process. Strong convergence of iterative sequences generated in the purposed iterative process is obtained in a real Banach space.

In this paper, two new iterative schemes are introduced in Hilbert space. They can be used to find a common element of the set of solutions of an equilibrium problem and the set of fixed point of the nonexpansive mapping. Under suitable conditions, some weak and strong convergence theorems are obtained.

We look for geometric structures which underlie both the 'classical' geometric and more modern 'order theoretic' conditions for a Banach space (dual space) to have the weak (weak*) fixed point property; that is, for every nonexpansive self-mapping of a nonempty weak (weak*) compact convex subset to have a fixed point.