Fixed point index and chain approximations

Retracts, fixed point index and differential equations

Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions. Retractos, ı́ndice de punto fijo y ecuaciones d...

Fixed Point Index in Symmetric Products

Let U be an open subset of a locally compact metric ANR X and let f : U → X be a continuous map. In this paper we study the fixed point index of the map that f induces in the n-symmetric product of X, Fn(X). This index can detect the existence of periodic orbits of period ≤ n of f , and it can be used to obtain the Euler characteristic of the n-symmetric product of a manifold X, χ(Fn(X)). We co...

Fixed Point Index for Composite Type Maps

An index theory is presented for compact absorbing contractive Jc or SJc maps and several new fixed point theorems are given for such maps. AMS(MOS) subject classification: 47H10

THE FIXED POINT INDEX AND ASYMPTOTIC FIXED POINT THEOREMS FOR ft-SET-CONTRACTIONS

Towards Viscosity Approximations of Hierarchical Fixed-point Problems

We introduce methods which seem to be a new and promising tool in hierarchical fixedpoint problems. The goal of this note is to analyze the convergence properties of these new types of approximating methods for fixed-point problems. The limit attained by these curves is the solution of the general variational inequality, 0 ∈ (I −Q)x∞ +NFixP(x∞), where NFixP denotes the normal cone to the set of...