An integrodifferential equation with fractional derivatives in the nonlinearities is studied in this article, and some sufficient conditions for existence and uniqueness of a solution for the equation are established by contraction mapping principle.

We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.

We show that two multiple stochastic integrals I n (f n), I m (g m) with respect to the solution (M t) t2I R + of a deterministic structure equation are independent if and only if two contractions of f n and g m , denoted as f n 0 1 g m , f n 1 1 g m , vanish almost everywhere.

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.