Best Approximation, Invariant Measures, and Fixed Points

Invariant Points of Best Approximation and Best Simultaneous Approximation

In this paper we generalize and extend BrosowskiMeinardus type results on invariant points from the set of best approximation to the set of best simultaneous approximation, which is not necessarily starshaped. As a consequence some results on best approximation are deduced. The proved results extend and generalize some of the results of R. N. Mukherjee and V. Verma [Publ. de l’Inst. Math. 49(19...

Common Fixed Points, Invariant Approximation and Generalized Weak Contractions

Fixed Points and Best Approximation in Menger Convex Metric Spaces

Nonexpansive mappings have been studied extensively in recent years by many authors.The first fixed point theorem of a general nature for nonlinear nonexpansive mappings in noncompact setting were proved independently by Browder [8] and Gohde [12]. Later on, Kirk [17] proved the same results under slightly weaker assumptions. A fundamental problem in fixed point theory of nonexpansive mappings ...

Invariant Points and ε-Simultaneous Approximation

Invariant manifolds near hyperbolic fixed points

In these notes we discuss obstructions to the existence of local invariant manifolds in some smoothness class, near hyperbolic fixed points of diffeomorphisms. We present an elementary construction for continuously differentiable invariant manifolds, that are not necessarily normally hyperbolic, near attracting fixed points. The analogous theory for invariant manifolds near hyperbolic equilbria...