Dashmir Mejdi

Existence of a Half-Iterate of the Exponential Map

We consider the classical problem of a compositional square root of the exponentialmap: a function φ with φ ◦ φ = exp. We first give a short, entirely elementary proof that astrictly increasing solution exists on R, using nothing beyond single-variable calculus. Suchsolutions are...

An Invariant-Strip Barrier for Gevrey-1 Regularity

If a contracting family of maps has jointly Gevrey-1 derivatives, does its fixed-pointfamily inherit the same factorial derivative-growth bound? The classical answer to thisshape of question is Cauchy’s majorant method: build an explicit dominating series andcompare term by term....

Cubic Stability via Two-Uniform Smoothness

Let a fixed point of a family of maps carry a leading cubic correction, Ts (x) − fs =(x − fs ) + Φs (x − fs ). If Φs is a restoring force — negative in the appropriate sense on theunit sphere, with controlled remainder — is the fixed point stable? On Hilbert space this iselementa...

Uniqueness of the Canonical Half-Iterate

A companion note (Existence of a Half-Iterate of the Exponential Map) stated, withoutproof, the Trappmann–Kouznetsov criterion singling out a canonical holomorphic half-iterateof exp, and remarked that its uniqueness half has been independently re-derived by twostructurally diffe...