Let X be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from X to X∗, and C be a closed convex subset of X which is also a sunny nonexpansive retract of X, and T : C → X a non-expansive mapping satisfying the weakly inward condition and F (T ) = ∅, and f : C → C be a fixed contractive mapping. The sequence {xn} is given by xn+1 = P (αnf(xn) + (1− αn)...

Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of E, f : C → C a contractive mapping or a weakly contractive mapping , and T : C → C nonexpansive mapping with the fixed point set F T / ∅. Let {xn} be generated by a...

In this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in CAT(0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...

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...

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

and Applied Analysis 3 Remark 1.6. The examples of weak relatively uniformly nonexpansive multivalued mapping can be found in Su 1 and Homaeipour and Razani 2 . Let E be a real Banach space, and let E∗ be the dual space of E. Let f be a bifunction from C × C to R. The equilibrium problem is to find x̂ ∈ C such that fx̂, y ≥ 0, ∀y ∈ C. 1.3 The set of solutions of 1.3 is denoted by EP f . Given a m...

Let X be a real Banach space, C a nonempty closed convex subset of X, and T : C → C a mapping. Recall that T is nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖ for all x, y ∈ C. Let Ti : C → C, i 1, 2, . . . , r, be nonexpansive mappings. Let Fix Ti denote the fixed points set of Ti, that is, Fix Ti : {x ∈ C : Tix x}, and let F : ⋂r i 1Fix Ti . For a given x1 ∈ C, and a fixed r ∈ N N denote the set of all ...

LetH be a real Hilbert space with inner product 〈·, ·〉 and norm ‖ · ‖, and let C be a nonempty closed convex subset of H. Recall that a mapping T : H → H is said to be nonexpansive if ‖Tx−Ty‖ ≤ ‖x−y‖ for all x, y ∈ H. The set of fixed points of T is Fix T : {x ∈ H : Tx x}. T : H → H is said to be quasi-nonexpansive if Fix T is nonempty and ‖Tx − p‖ ≤ ‖x − p‖ for all x ∈ H and p ∈ Fix T . Given ...

Let K be a subset of a real normed linear space E and let T be a self-mapping on K . T is said to be nonexpansive provided ‖Tx−Ty‖ ‖x− y‖ for all x, y ∈ K . Fixed-point iteration process for nonexpansive mappings in Banach spaces including Mann and Ishikawa iteration processes has been studied extensively by many authors to solve the nonlinear operator equations in Hilbert spaces and Banach spa...

Huang and Zhang cite{Huang} have introduced the concept of cone metric space where the set of real numbers is replaced by an ordered Banach space. Shojaei cite{shojaei} has obtained points of coincidence and common fixed points for s-Contraction mappings which satisfy generalized contractive type conditions in a complete cone metric space.In this paper, the notion of complete cone metric ...