In this paper, we construct a Liapunov functional for a system of nonlinear integral equations. From that Liapunov functional we are able to establish the existence of periodic solutions to the system by applying some well-known fixed point theorems for the sum of a nonlinear contraction mapping and compact operator.

This paper studies the income fluctuation problem without imposing bounds on utility, assets, income or consumption. We prove that the Coleman operator is a contraction mapping over the natural class of candidate consumption policies when endowed with a metric that evaluates consumption differences in terms of marginal utility. We show that this metric is complete, and that the fixed point of t...

We define the multivalued Reich (G, ρ)-contraction mappings on a modular function space. Then we obtain sufficient conditions for the existence of fixed points for such mappings. As an application, we introduce a ρ-valued Bernstein operator on the set of functions f : [0, 1] → Lρ and then give the modular analogue to Kelisky-Rivlin theorem. c ©2016 All rights reserved.

We describe a new proof of the exponential contraction of the Feigenbaum renormalization operator in the hybrid class of the Feigenbaum fixed point. The proof uses the non existence of invariant line fields in the Feigenbaum tower (C. McMullen), the topological convergence (D. Sullivan), and a new infinitesimal argument, different from previous methods by C. McMullen and M. Lyubich.

The well known contraction mapping principle or Banach’s fixed point theorem asserts: The method for successive substitutions converges only linearly to a fixed point of an operator equation in a Banach space setting [5], [7]. In practice, if Newton’s method is used one ignores the additional information about the contraction mapping information. Werner in [9] provided a local analysis for a Ne...

Different (not only by sign) affine connections are introduced for con-travariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual space and commuting with the covariant and with the Lie-differential operator. Classification of the linear transports on the basis of the connections between the connections is giv...

It has been established quite recently [1], that a contraction T , having finite defects (rank (I − T T ), rank (I − TT ) < ∞) and the spectrum σ(T ) not filling in the closed unit disk D, is similar to a normal operator if and only if C1(T ) = sup λ6∈σ(T ) ||(T − λ)|| · dist(λ, σ(T )) < ∞. It was shown later [9], that the “only if” part of the assertion is no longer true if T is not a contract...

Deformation theory requires solving Maurer-Cartan equation (MCE) associated to an DGLA (L-infinity algebra). The universal solution of [HS] is obtained iteratively, as a fixed point of a contraction, analogous to the Picard method. The role of the Kuranishi functor in this construction is emphasized. The parallel with Lie theory suggests that deformation theory is a higher “dimensional” version...

We gain tight rigorous bounds on the renormalization fixed point for period doubling in families of unimodal maps with degree 4 critical point. use a contraction mapping argument to bound essential eigenfunctions and eigenvalues linearization operator controlling scaling added noise. Multi-precision arithmetic directed rounding is used operations space analytic functions yielding power series c...

For a large class of unitarily invariant reproducing kernel functions K on the unit ball \(\mathbb B_d\) in C^d\), we characterize K-inner as admitting suitable transfer function realization. We associate with each K-contraction T ∈ L(H)d canonical operator-valued and extend uniqueness theorem Arveson for minimal K-dilations to our setting. thus generalize results Olofsson m-hypercontractions d...