In this paper, we prove some …xed point theorems for two hybrid pairs of mappings in 2-metric spaces by using some weaker conditions. Mathematics subject classi…cation: 47H10, 54H25. Key words and phrases: Coincidence point, common …xed point, compatible maps, weak commutativity of type (KB) :

Existence of critical renormalization group trajectory for a hierarchical Ising model in 4 dimensions is shown. After 70 iterations of renormalization group transformations, the critical Ising model is mapped into a vicinity of the Gaussian xed point. Convergence of the subsequent trajectory to the Gaussian xed point is shown by power decay of the eeective coupling constant. The analysis in the...

In this paper we give a numerical description of the neighbourhood of a xed point of a symplectic map undergoing a transition from linear stability to complex instability i e the so called Hamiltonian Hopf bifurcation We have considered both the direct and inverse cases The study is based on the numerical computation of the Lyapunov families of invariant curves near the xed point We show how th...

We de ne a value-based modal -calculus, built from rst-order formulas, modalities, and xed point operators parameterized by data variables, which allows to express temporal properties involving data. We interpret this logic over CRL terms de ned by linear process equations. The satisfaction of a temporal formula by a CRL term is translated to the satisfaction of a rst-order formula containing p...

It is critical to have an induction method for reasoning about re-cursive programs expressed as xed points, for otherwise our reasoning ability is severely impaired. The xed point induction rule developed by deBakker and Scott is one such well known principle. Here we propose a new induction method, computational induction , which is an induction on the computation process. Computational induct...

S. Vassiliadis K. Bertels G. G. Pechanek E.E. Dept Dept. Gestion de l'Entreprise DSP Architecture/Development T.U. Delft, Delft Univ. of Namur IBM Corporation The Netherlands 2628 CD 5000 Namur, Belgium RTP, N.C. 27709 USA Abstract In this paper we investigate the possibility of constructing xed point units using feed-forward neural networks. We investigate the possibility of constructing small...

The problem of transition to chaos, i.e. the destruction of invariant circles or KAM (Kolmogorov-Arnold-Moser) curves, in area preserving nontwist maps is studied within the renormalization group framework. Nontwist maps are maps for which the twist condition is violated along a curve known as the shearless curve. In renormalization language this problem is that of nding and studying the xed po...

We unveil new results based on measurement that guarantee the existence of unique xed points which need not be maximal. In addition, we establish that least xed points are always attractors in the topology, and then explore the consequences of these ndings in analysis. In particular, an extension of the Banach xed point theorem on compact metric spaces 3] is obtained.

The relationship between xed point theory and K {theory is explained, both classical Nielsen theory (versus K 0) and 1{parameter xed point theory (versus K 1). In particular, various zeta functions associated with suspension ows are shown to come in a natural way as \traces" of \torsions" of Whitehead and Reidemeister type.