In this paper, we introduce a modified three-step iterative scheme for approximating a fixed point of nonexpansive mappings in the framework of uniformly smooth Banach spaces and the reflexive Banach spaces which have a weakly continuous duality map, respectively. we establish the strong convergence of the modified three-step iterative scheme. The results improve and extend recent ones given by...

where / is a mapping of X into its adjoint space X* such that for all u in X, (J(u)} ^)=|M| 2 d ||/(^)|| HMI* In some recent papers ([7], [8], [9]), we have presented an existence theory for solutions of nonlinear functional equations in uniformly convex Banach spaces X involving nonexpansive and accretive mappings. These results were obtained by interweaving the fixed point theory of nonexpans...

cycle time, discrete event system, fixed point, max-plus semiring, nonexpansive map, topical function Discrete event systems provide a useful abstraction for modelling a wide variety of systems: digital circuits, communication networks, manufacturing plants, etc. Their dynamics—stability, equilibrium states, cyclical behaviour, asymptotic average delays—are of vital importance to system designe...

We investigate necessary and sufficient conditions for a nonexpansive map $f$ on Banach space $X$ to have surjective displacement, that is, $f - \mathrm{id}$ onto $X$. In particular, we give computable condition when is finite dimensional with polyhedral norm. similar fixed point of norm be unique. also consider applications nonlinear Perron-Frobenius theory suggest some additional displacement...

we introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition fo...

Let C be a nonempty closed convex subset of a real Hilbert space H. Let S : C → C be an asymptotically nonexpansive map in the intermediate sense with the fixed point set F (S). Let A : C → H be a Lipschitz continuous map, and V I(C,A) be the set of solutions u ∈ C of the variational inequality 〈Au, v − u〉 ≥ 0, ∀v ∈ C. The purpose of this work is to introduce a hybrid extragradient-like approxi...

Let H be a Hilbert space and let C be a closed convex nonempty subset of H and [Formula: see text] a non-self nonexpansive mapping. A map [Formula: see text] defined by [Formula: see text]. Then, for a fixed [Formula: see text] and for [Formula: see text], Krasnoselskii-Mann algorithm is defined by [Formula: see text] where [Formula: see text]. Recently, Colao and Marino (Fixed Point Theory App...

Recall that a map F: D/X X on a Banach space (X, & }&) is called ``nonexpansive'' if &F(a)&F(b)& &a&b& for all a, b # D. Here we shall be interested in X=l1(Z), the Banach space of biinfinite absolutely summable real sequences (an | n # Z) , with &a&1 := n # Z |an |. As usual, l1 (Z)= [a # l1(Z) : an 0 \n # Z], and we shall be interested in nonexpansive maps F: l1 (Z) l + 1 (Z). Our maps will a...

A common fixed-point generalization of the results of Dotson, Tarafdar, and Taylor is obtained which in turn extends a recent theorem by Jungck and Seasa to locally convex spaces. As applications of our work, we improve and unify well-known results on fixed points and common fixed points of beat approximation. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords--common fixed point, Best ...

This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a Banach space and its dual. In this paper, we establish several new results and also give improved proofs of some known ones in both the general and the special ...