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...

The purpose of this paper is to extend the notion of well-posedness of fixed point problem for a mapping to a hybrid pair of mappings. Also, we prove a general common fixed point theorem for a pair of D-mappings for which the fixed point problem is well posed.

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...

Let (ρ0, ρ1) and (ρ ′ 0, ρ ′ 1) be two ordered pairs of permutations in Sn and let t be a divisor of n. The Yelton-Gaines conjecture states that if at least one of these four permutations is a product of n/t disjoint t-cycles, and if there is a strong isomorphism (definition below) φ : 〈ρ0, ρ1〉 → 〈ρ0, ρ1〉 between the two subgroups of Sn generated by the elements in each ordered pair, then there...

in this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and  coincidence point  theorems on partially ordered fuzzy metric spaces are proved. also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.