Let A and B be uniform algebras on first-countable, compact Hausdorff spaces X and Y , respectively. For f ∈ A, the peripheral spectrum of f , denoted by σπ(f) = {λ ∈ σ(f) : |λ| = ‖f‖}, is the set of spectral values of maximum modulus. A map T : A → B is weakly peripherally multiplicative if σπ(T (f)T (g)) ∩ σπ(fg) 6= ∅ for all f, g ∈ A. We show that if T is a surjective, weakly peripherally mu...

In this paper the existence and approximation of a unique common fixed point of two families of weakly compatible self-maps on a complete metric space are investigated. An example is presented to show that our results for the mappings considered satisfying non-linear contractive type conditions are genuine generalizations of the recent result for metric spaces [B. Singh, S. Jain, A fixed point ...

This is the third part of our project initiated in [LW1] on the study of the weakly convergent sequence of smooth (or certain classes of weak) solutions to the heat equation of harmonic maps or approximated harmonic maps (i.e. the negative gradient ow of the generalized Ginzburg-Landau functionals). The general situation for the heat ow of harmonic maps is as follows. Let un(x; t) : M R+ ! N be...

A KKM space is an abstract convex space satisfying the KKM principle. We obtain variants of the KKM principle for KKM spaces related to weakly KKM maps and indicate some applications of them. These results properly generalize the corresponding ones in G-convex spaces and φA-spaces X,D; {φA}A∈〈D〉 . Consequently, results by Balaj 2004, Liu 1991, and Tang et al. 2007 can be properly generalized an...

In this paper, we introduce the notion of complex valued Gmetric spaces and prove a common fixed point theorem for weakly compatible maps in this newly defined spaces. Mathematics Subject Classification (2000): 47H10, 54H25.

Weakly interacting lattices of coupled maps can be modeled as ordinary coupled map lattices separated from each other by boundary regions with small coupling parameters. We demonstrate that such weakly interacting lattices can nevertheless have unexpected and striking effects on each other. Under specific conditions, particular stability properties of the lattices are significantly influenced b...

We prove that a weakly Dirac-harmonic map from a Riemann spin surface to a compact hypersurface N ⊂ R is smooth. 2000 Mathematics Subject Classification: 58J05, 53C27.

A common coincidence point theorem for R-weakly commuting mappings is obtained. Our result extend several ones existing in literature. 2000 Mathematics Subject Classification. 54H25.