If A(z) is a function of a real or complex variable with values in the space B(X) of all bounded linear operators on a Banach space X with each A(z) g-Drazin invertible, we study conditions under which the g-Drazin inverse AD(z) is differentiable. From our results we recover a theorem due to Campbell on the differentiability of the Drazin inverse of a matrix valued function and a result on diff...

Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of G~teaux, Fr6chet, and Hadamard are singled out from the general framework of cr-directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equ...

Two functional equations are considered that are motivated by three considerations: work in utility theory and psychophysics, questions concerning when pairs of degree 1 homogeneous functions can be homomorphic and calculating their homomorphisms, and the link of the latter questions to quasilinear mean values. The first equation is h(σ(y)x + [1 - σ(y)]y) = τ(y)h(x) + [1 - τ(y)]h(y) (x ≥ y ≥ 0)...

Sufficient conditions are given for a mapping to be γ -G inverse differentiable. Constrained implicit function theorems for γ -G inverse differentiable mappings are obtained, where the constraint is taken to be either a closed convex cone or a closed subset. A theorem without assuming the γ -G inverse differentiability in a finite-dimensional space is also presented.

We give a complete characterization of all Kleinian groups G, acting on hyperbolic space Hn, that admit non-constant G-automorphic quasimeromorphic mappings, for any n ≥ 2. We also address the related problem of existence of qm-mappings on manifolds and prove the existence of such mappings on manifolds with boundary, of low differentiability class.

The theory of generic differentiability of convex functions on Banach spaces is by now a well-explored part of infinite-dimensional geometry. All the attempts to solve this kind of problem have in common, as a working hypothesis, one special feature of the finite-dimensional case. Namely, convex functions are always considered to be defined on convex sets with nonempty interior. But typically, ...

We provide an improvement of the maximum principle Pontryagin Optimal Control problems. establish differentiability properties value function problems with assumptions as low possible. Notably, we lighten by using G\^ateaux and Hadamard differentials.