Search results for "Fixed Point"

On Fixed Point (Trial) Methods for Free Boundary Problems

1992

In this note we consider the trial methods for solving steady state free boundary problems. For two test examples (electrochemical machining and continuous casting) we discuss the convergence of a fixed point method. Moreover, using the techniques of shape optimization we introduce a modification of the method, which gives us superlinear convergence rate. This is also confirmed numerically.

A new approximation procedure for fractals

2003

AbstractThis paper is based upon Hutchinson's theory of generating fractals as fixed points of a finite set of contractions, when considering this finite set of contractions as a contractive set-valued map.We approximate the fractal using some preselected parameters and we obtain formulae describing the “distance” between the “exact fractal” and the “approximate fractal” in terms of the preselected parameters. Some examples and also computation programs are given, showing how our procedure works.

Invariant approximation results in cone metric spaces

2011

‎Some sufficient conditions for the existence of fixed point of mappings‎ ‎satisfying generalized weak contractive conditions is obtained‎. ‎A fixed‎ ‎point theorem for nonexpansive mappings is also obtained‎. ‎As an application‎, ‎some invariant approximation results are derived in cone metric spaces‎.

Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations

2012

We derive some new coincidence and common fixed point theorems for self-mappings satisfying a generalized contractive condition in partially ordered metric spaces. As applications of the presented theorems, we obtain fixed point results for generalized contraction of integral type and we prove an existence theorem for solutions of a system of integral equations.

On Boundary Conditions for Wedge Operators on Radial Sets

2008

We present a theorem about calculation of fixed point index for k-$\psi$-contractive operators with 0 < k <1 defined on a radial set of a wedge of an infinite dimensional Banach space. Then results on the existence of eigenvectors and nonzero fixed points are obtained.

Singular Double Phase Problems with Convection

2020

We consider a nonlinear Dirichlet problem driven by the sum of a $p$ -Laplacian and of a $q$ -Laplacian (double phase equation). In the reaction we have the combined effects of a singular term and of a gradient dependent term (convection) which is locally defined. Using a mixture of variational and topological methods, together with suitable truncation and comparison techniques, we prove the existence of a positive smooth solution.

Fixed point theory for almost convex functions

1998

Traditionally, metric fixed point theory has sought classes of spaces in which a given type of mapping (nonexpansive, assymptotically or generalized nonexpansive, uniformly Lipschitz, etc.) from a nonempty weakly compact convex set into itself always has a fixed point. In some situations the class of space is determined by the application while there is some degree of freedom in constructing the map to be used. With this in mind we seek to relax the conditions on the space by considering more restrictive types of mappings.

Weak convergence theorems for asymptotically nonexpansive mappings and semigroups

2001

Multiplicity of fixed points and growth of ε-neighborhoods of orbits

2012

We study the relationship between the multiplicity of a fixed point of a function g, and the dependence on epsilon of the length of epsilon-neighborhood of any orbit of g, tending to the fixed point. The relationship between these two notions was discovered before (Elezovic, Zubrinic, Zupanovic) in the differentiable case, and related to the box dimension of the orbit. Here, we generalize these results to non-differentiable cases introducing a new notion of critical Minkowski order. We study the space of functions having a development in a Chebyshev scale and use multiplicity with respect to this space of functions. With the new definition, we recover the relationship between multiplicity o…

Analysis and approximation of one-dimensional scalar conservation laws with general point constraints on the flux

2016

We introduce and analyze a class of models with nonlocal point constraints for traffic flow through bottlenecks, such as exits in the context of pedestrians traffic and reduction of lanes on a road under construction in vehicular traffic. Constraints are defined based on data collected from non-local in space and/or in time observations of the flow. We propose a theoretical analysis and discretization framework that permits to include different data acquisition strategies; a numerical comparison is provided. Nonlocal constraint allows to model, e.g., the irrational behavior (" panic ") near the exit observed in dense crowds and the capacity drop at tollbooth in vehicular traffic. Existence …