in this paper, using the best proximity theorems for an extensionof brosowski's theorem. we obtain other results on farthest points. finally, wedene the concept of e- farthest points. we shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (x; ||.||). if z in w is a e-farthest point from an x in x, then z is also a-best ...

begin{abstract}using the fixed point method, we prove the generalized hyers--ulam--rassiasstability of the following functional equation in multi-banach spaces:begin{equation} sum_{ j = 1}^{n}fbig(-2 x_{j} + sum_{ i = 1, ineq j}^{n} x_{i}big) =(n-6) fbig(sum_{ i = 1}^{n} x_{i}big) + 9 sum_{ i = 1}^{n}f(x_{i}).end{equation}end{abstract}

A topological group G has the Approximate Fixed Point (AFP) property on a bounded convex subset C of a locally convex space if every continuous affine action of G on C admits a net ( x i ) , x i ∈ C , such that x i - g ⁢ x i ⟶ 0 for all g ∈ G . In this work, we study the relationship between this property and amenability.

In this paper we propose a derivative-free iterative method for the approximate solution of a nonlinear inverse problem Fx = y. In this method the iterations are defined as Gxk+1 = Gxk +(Sy−SFxk), where G is an easily invertible operator and S is an operator from a data space to a solution space. We give general suggestions for the choice of operators G and S and show a practically relevant exa...

In this paper we generalize to unbounded convex subsets C of hyperbolic spaces results obtained by W.A. Kirk and R. Esṕınola on approximate fixed points of nonexpansive mappings in product spaces (C×M)∞, where M is a metric space and C is a nonempty, convex, closed and bounded subset of a normed or a CAT(0)-space. We extend the results further, to families (Cu)u∈M of unbounded convex subsets of...

We give ruler and compass constructions of three Archimedean circles in an arbelos, each with the endpoints of a diameter on the smaller semicircles. In the first case, the diameter contains the intersection of the defining smaller semicircles of the arbelos. In the second case, these endpoints are the intersections of the smaller semicircles with the lines joining the endpoints of the base of ...

In 1984, M. M. Marsh gave conditions under which the inverse limit of an inverse sequence of fans has the fixed point property. In this paper we give an extension of that result. 1. Definitions and notation By a space we mean a topological space. A continuum is a nonempty compact connected metric space. By a map we mean a continuous function. A fixed point of a map f : X → X is a point x ∈ X su...

in this paper, we study the existence of coupled coincidence andcoupled common fixed points for single-valued and fuzzy mappingsunder a contractive condition in metric space. presented theoremsextend and improve the main results of abbas and$acute{c}$iri$acute{c}$ {itshape et al.} [m. abbas, l.$acute{c}$iri$acute{c}$, {itshape et al.}, coupled coincidenceand common fixed point theorems for hybr...

We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a continues region (Imprecise model) or a finite set of points (Indecisive model). Given a set of inexact points in one of Imprecise or Indecisive models, we wish to provide a lower-bound on the diameter...

We introduce the concepts of ∗-diminishing orbital diameters and diminishing orbital diameters for a pair (f ,g) of self mappings in metric spaces and prove common fixed point theorems for these mappings. The results obtained in this paper extend properly the result of Fisher (1978). 2000 Mathematics Subject Classification. 54H25.