R. Kargar

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math.CV2026

Characterizations of extremal hyperbolic rates via Herglotz measures and Koenigs linearization

Rahim Kargar

Let $g : D \to D$ be a hyperbolic holomorphic self-map of the unit disk with Denjoy--Wolff point $τ \in \partial D$ and angular derivative $α \in (0, 1)$ . We say t…

math.CV2026

Higher-order Volterra-type integral operator on Hardy and Bergman spaces

Rahim Kargar

We investigate the higher-order Volterra-type integral operator $T_{g, n}$ on the unit disk, defined for $n \in N$ by \[ T_{g,n}[f](z) := \underbrace{\int_{0}^{z}\int_{0}^{t_1…

math.CV2026

Variable exponent modulus in symmetric domains

Rahim Kargar

We develop a rigorous variational theory for the modular variable-exponent modulus of curve families in two symmetric geometries: annuli $A (r_{1}, r_{2}) \subset R^{n}$ with radial…

math.CV2026

On a certain subclass of strongly starlike functions

R. Kargar, J. SokÃ³Å, H. Mahzoon

Let $S^{*} (I^\pm_{1}, I^\pm_{2})$ , where $I^\pm_{1}, I^\pm_{2} \in (0, 1]$ , represent the class of functions $f$ that are analytic in the open unit disk $D$ , normalized by $f(0) = f'(0…

math.CV2025

Volterra type integral operator and analytic function spaces

Rahim Kargar

We investigate the geometric properties of the Volterra-type integral operator \begin{equation*} T_g[f](z) = \int_{0}^{z} f(s)\, g'(s)\, ds, \quad |z|<1, \end{equation*} acting on…

math.CV2024

Formulas for the visual angle metric

Masayo Fujimura, Rahim Kargar, Matti Vuorinen

We prove several new formulas for the visual angle metric of the unit disk in terms of the hyperbolic metric and apply these to prove a sharp Schwarz lemma for the visual angle met…