We prove a type of converse of the Banach contraction mapping theorem for metric spaces: if X is a T 1 topological space and f : X ! X is a function with unique xed point a such that f n (x) converges to a for each x 2 X , then there exists a distance function d on X such that f is a contraction on the complete ultrametric space (X; d) with contractivity factor 1 2. We explore properties of the...

Some theorists have developed formal approaches to truth that depend on counterexamples to the structural rules of contraction. Here, we study such approaches, with an eye to helping them respond to a certain kind of objection. We define a contractive relative of each noncontractive relation, for use in responding to the objection in question, and we explore one example: the contractive relativ...

We provide an overview of recent results concerning the dynamics of polygonal billiards with a contractive reflection law.

We present a theory concerning the realization of capital gains where ownership and control are linked as in Holmes and Schmitz (1995). The model developed is a version of a Lucas-tree economy in which the productivity of a technology depends on the ownership of the technology. The existence and uniqueness of equilibrium follow from the Contraction Mapping Theorem. The theory implies that imped...

In this paper the concept of a fuzzy contraction mapping on a fuzzy metric space is introduced and it is proved that every fuzzy contraction mapping on a complete fuzzy metric space has a unique fixed point.

In this paper, we introduce the concepts of qpb-cyclic-Banach contraction mapping, qpb-cyclic-Kannan mapping and qpb-cyclic β-quasi-contraction mapping and establish the existence and uniqueness of fixed point theorems for these mappings in quasi-partial b-metric spaces. Some examples are presented to validate our results. c ©2016 All rights reserved.

In this paper we introduce a generalization of Meir-Keeler contraction forrandom mapping T : Ω×C → C, where C be a nonempty subset of a Banachspace X and (Ω,Σ) be a measurable space with being a sigma-algebra of sub-sets of. Also, we apply such type of random fixed point results to prove theexistence and unicity of a solution for an special random integral equation.

Let (X,H) be a pair of a smooth rational surface X and an ample divisor H on X . Assume that (KX , H) < 0. Let MH(r, c1, χ) be the moduli space of semi-stable sheaves E of rk(E) = r, c1(E) = c1 and χ(E) = χ. To consider relations between moduli spaces of different invariants is an interesting problem. If (c1, H) = 0 and χ ≤ 0, then Maruyama [Ma2], [Ma3] studied such relations and constructed a ...

The submartingale convergence theorem is often described as a stochastic analogue to the bounded convergence theorem for monotone sequences of real numbers. We define an alternative process which is a stochastic analogue to an iterative contraction process. A general convergence theorem is presented, with an extension to multivariate processes. The convergence theorem functions in a manner simi...