Construction of Fixed Points by Some Iterative Schemes

Construction of Fixed Points by Some Iterative Schemes

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...

Frequency selective N.M.R. pulse sequences generated by iterative schemes with multiple fixed points

Frequency selective N.M.R. pulse sequences generated by iterative schemes with multiple fixed points H. Cho a b c , K.T. Mueller a b , A.J. Shaka a b d & A. Pines a b a Materials and Chemicals Sciences Division, Lawrence Berkeley Laboratory, 1 Cyclotron Road, Berkeley, California, 94720, U.S.A. b Department of Chemistry, University of California, Berkeley, California, 94720, U.S.A. c Laboratori...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

An abstract point of view on iterative approximation schemes of fixed points for multivalued operators

In this paper we will present an abstract point of view on iterative approximation schemes of fixed points for multivalued operators. More precisely, we suppose that the algorithms are convergent and we will study the impact of this hypothesis in the theory of operatorial inclusiosns: data dependence, stability and Gronwall type lemmas. Some open problems are also presented.

Approximating Fixed Points by a Two-Step Iterative Algorithm

In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corre...