Layout of facilities with some fixed points

Layout of facilities with some fixed points

This paper deals with the location of facilities or “movable” points on a planar area, on which there already exist fixed points. The minimax criterion for optimality is used and distances among points are assumed to be rectilinear. Two very efficient algorithms for the solution of the problem are presented. One is based on a univariate search, and the other on a steepest descent method. Some c...

Some Mathematical Aspects of InformationTechnology : Fixed Points and the Formal

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...

Some Sufficient Conditions for Fixed Points of Multivalued Nonexpansive Mappings

We show some sufficient conditions on a Banach space X concerning the generalized James constant, the generalized Jordan-von Neumann constant, the generalized Zbagănu constant, the coefficient ε̃0 X , the weakly convergent sequence coefficientWCS X , and the coefficient of weak orthogonality, which imply the existence of fixed points for multivalued nonexpansive mappings. These fixed point theor...

Approximating fixed points of generalized nonexpansive mappings