In our 2006 paper with D. Butnariu, it was shown that the convergence of iterates a nonexpansive self-mapping complete metric space is stable in presence summable computational errors. present paper, we establish such results for monotone mappings.

and Applied Analysis 3 where R is the set of all real numbers; in particular, J(−x) = −J(x) for all x ∈ E ([28]). We say that a Banach space E has a weakly sequentially continuous duality mapping if there exists a gauge function φ such that the duality mapping Jφ is single valued and continuous from the weak topology to the weak topology; that is, for any {xn} ∈ E with xn ⇀ x, Jφ(xn) ∗ ⇀ Jφ(x)....

Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand Abstract In this article, we introduce a new mapping generated by infinite family of nonexpansive mapping and infinite real numbers. By means of the new mapping, we prove a strong convergence theorem for finding a common element of the se...

Let X be a real Banach space and let C be a nonempty closed convex subset of X. A selfmapping T : C → C is said to be nonexpansive if ‖Tx−Ty‖ ≤ ‖x−y‖, for all x, y ∈ C.A point x ∈ C is a fixed point of T provided Tx x. Denote by Fix T the set of fixed points of T ; that is, Fix T {x ∈ C : Tx x}. It is assumed throughout this paper that T is a nonexpansive mapping such that Fix T / ∅. Constructi...

Let K be a nonempty closed convex subset of a real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti : K → E, i = 1, 2, · · · , N be a family of nonexpansive mappings which are weakly inward with F = ⋂N i=1 F (Ti) 6= ∅. Let f : K → K be a fixed contractive mapping. For given x0...

this paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   the main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...

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...

the aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. our result is generalize and extends the corresponding result of jhade et al. [p.k. jhade, a.s. saluja and r. kushwah, coincidence and fixed points of ...

and Applied Analysis 3 a constant c > 0 such that δ ε ≥ cε for all ε ∈ 0, 2 ; see 12, 13 for more details. Observe that every p-uniformly convex is uniformly convex. One should note that no Banach space is p-uniformly convex for 1 < p < 2. It is well known that a Hilbert space is 2-uniformly convex, uniformly smooth. For each p > 1, the generalized duality mapping Jp : E → 2E is defined by Jp x...