Common fixed points of commuting holomorphic maps of the hyperball.

Fixed Points of Commuting Holomorphic Maps without Boundary Regularity

We identify a class of domains of C in which any two commuting holomorphic self-maps have a common fixed point.

Fixed Points and Periodic Points of Semiflows of Holomorphic Maps

Let φ be a semiflow of holomorphic maps of a bounded domain D in a complex Banach space. The general question arises under which conditions the existence of a periodic orbit of φ implies that φ itself is periodic. An answer is provided, in the first part of this paper, in the case in which D is the open unit ball of a J∗-algebra and φ acts isometrically. More precise results are provided when t...

Commuting Functions with No Common Fixed Points)

Introduction. Let/and g be continuous functions mapping the unit interval / into itself which commute under functional composition, that is, f(g(x)) = g(f(x)) for all x in /. In 1954 Eldon Dyer asked whether/and g must always have a common fixed point, meaning a point z in / for which f(z) = z=g(z). A. L. Shields posed the same question independently in 1955, as did Lester Dubins in 1956. The p...

Sub-Compatible Maps, Weakly Commuting Maps and Common Fixed Points in Cone Metric Spaces

The purpose of this paper is to obtain some common fixed point theorems under weaker conditions such as sub compatible mappings and weakly commuting with respect g in the setting of non normal cone metric space.

Common Fixed Points of Two Commuting Mappings in Complete Metric Spaces