Fixed point formula for holomorphic functions

Fixed Point Theorems for Infinite Dimensional Holomorphic Functions

This talk discusses conditions on the numerical range of a holomorphic function defined on a bounded convex domain in a complex Banach space that imply that the function has a unique fixed point. In particular, extensions of the Earle-Hamilton Theorem are given for such domains. The theorems are applied to obtain a quantitative version of the inverse function theorem for holomorphic functions a...

A fixed point theorem for discontinuous functions

We establish the following fixed point theorem. Let P be a non-empty polytope in the n-dimensional Euclidean space and let f be a function from P to P satisfying that for every x in P for which f(x) 6= x there exists a neighborhood of x in P such that for any y and z in this neighborhood the inner product of f(y)− y and f(z)− z is non-negative. Then there exists x∗ ∈ P satisfying f(x∗) = x∗, i....

Fixed Point Iterations for Real Functions

A Fixed Point Theorem for Analytic Functions

We denote that set by A(z,w,k) and (following [1]) call it the Apollonius circle of constant k associated to the points z and w. The set A(z,w,k) is a circle for all values of k other than 1 when it is a line. In this paper, we consider z,w ∈ U, show that if z = w, then necessarily A(z,w, √ (1−|w|2)/(1−|z|2)) meets the unit circle twice, consider the arc on the unit circle with those endpoints,...

Fixed Point Theory for Almost Convex Functions