R. Kargar

activity

20172026

most citedOn logarithmic coefficients of certain starlike functions related to the vertical strip

13 citations · 20 across the 24 of their papers we have counts for

collaborators

25 papers

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

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.CV2025

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.CV2023

On Harnack inequality and harmonic Schwarz lemma

Rahim Kargar

In this paper, we study the $(s, C (s))$ -Harnack inequality in a domain $G \subset R^{n}$ for $s \in (0, 1)$ and $C (s) \geq 1$ and present a series of inequalities related to $(s,…

math.MG2023

Intrinsic metrics defined with arithmetic and logarithmic mean values

Oona Rainio, Rahim Kargar

We introduce several new functions that measure the distance between two points $x$ and $y$ in a domain $G ⊊ R^{n}$ by using the arithmetic or the logarithmic mean of…

math.CV2023

Conformally invariant metrics and lack of Hölder continuity

Rahim Kargar, Oona Rainio

The modulus metric between two points in a subdomain of $R^{n}, n \geq 2,$ is defined in terms of moduli of curve families joining the boundary of the domain with a continuum…

math.CV2023

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…

math.CV2022★ 2 cited

Landen transformations applied to approximation

Rahim Kargar, Oona Rainio, Matti Vuorinen

We study computational methods for the approximation of special functions recurrent in geometric function theory and quasiconformal mapping theory. The functions studied can be exp…

math.CV2022

Intrinsic metrics in polygonal domains

D. Dautova, R. Kargar, S. Nasyrov +1

We study inequalities between the hyperbolic metric and intrinsic metrics in convex polygonal domains in the complex plane. Special attention is paid to the triangular ratio metric…

math.CV2020★ 2 cited

On quasiconformal close-to-convex harmonic mappings involving starlike functions

Zhi-Gang Wang, Xin-Zhong Huang, Zhi-Hong Liu +1

In the present paper, we discuss several basic properties of a class of quasiconformal close-to-convex harmonic mappings with starlike analytic part, such results as coefficient in…

math.CV2019

Notes on the norm of pre-Schwarzian derivatives on bi-univalent functions of order $α$

H. Mahzoon, R. Kargar

In the present paper we estimate the norm of the pre-Schwarzian derivative of bi-starlike functions of order $α$ where $α \in [0, 1)$ . Initially this problem was handled by Rahmatan e…

math.CV2019

A note on the paper "Tang et al. [Bull Iran Math Soc (2019) doi:10.1007/s41980-019-00262-y]"

M. M. Motamedinezhad, Rahim Kargar

Very recently Tang et al. [Bull Iran Math Soc (2019) doi:10.1007/s41980-019-00262-y] have studied some majorization results for two certain subclasses of the starlike functions ass…

math.CV2019

Notes on the norm of pre-Schwarzian derivatives of certain analytic functions

Rahim Kargar

In this paper, we obtain sharp bounds for the norm of pre--Schwarzian derivatives of certain analytic functions. Initially this problem was handled by H. Rahmatan, Sh. Najafzadeh a…

math.CV2019

On certain subclasses of close-to-convex functions related with the second-order differential subordination

Hesam Mahzoon, Rahim Kargar

Let $A$ be the family of analytic and normalized functions in the open unit disc $∣ z ∣ < 1$ . In this article we consider the following classes \begin{equation*} \mathcal{R}(…

math.CV2019

Further results for a subclass of univalent functions related with differential equation

Hesam Mahzoon, Rahim Kargar

Let $Ω$ denote the class of functions $f$ analytic in the open unit disc $Δ$ , normalized by the condition $f (0) = f^{'} (0) - 1 = 0$ and satisfying the inequality \begin{equation*} \left|zf'…

math.CV2018

On starlike functions related with the convex conic domain

R. Kargar, J. Sokół

In the present paper, we study a new subclass $M_{p} (α, β)$ of $p$ --valent functions and obtain some inequalities concerning the coefficients for the desired class. Also, by…

math.CV2018

On a certain subclass of strongly starlike functions

R. Kargar, J. Sokół, H. Mahzoon

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

math.CV2018

Some new inequalities for univalent functions

M. M. Motamedinezhad, R. Kargar

By use of a modified Nunokawa's lemma, we obtain some new conditions for univalence. Also, some sharp inequalities concerning univalent functions are presented.

math.CV2018

Some applications of differential subordination for certain starlike functions

R. Kargar, L. Trojnar-Spelina

We consider the class $S^{*} (q_{c})$ of normalized starlike functions $f$ analytic in the open unit disk $∣ z ∣ < 1$ that satisfying the inequality \begin{equation*} \left|\left(…

math.CV2018★ 13 cited

On logarithmic coefficients of certain starlike functions related to the vertical strip

Rahim Kargar

In the present paper two certain subclasses of the starlike functions associated with the vertical strip are considered. The main aim of this paper is to investigate some basic pro…

math.CV2018

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.CV2018★ 1 cited

Some inequalities for a certain subclass of starlike functions

R. Kargar, H. Mahzoon, N. Kanzi

In 2011, Sokół (Comput. Math. Appl. 62, 611--619) introduced and studied the class $S K (α)$ as a certain subclass of starlike functions, consists of all functions $f$ ($f(…

math.CV2018★ 1 cited

Further results for starlike functions related with Booth lemniscate

R. Kargar, A. Ebadian, L. Trojnar-Spelina

In this paper we investigate an interesting subclass $BS (α)$ ( $0 \leq α < 1$ ) of starlike functions in the unit disk $Δ$ . The class $BS (α)$ was introduced by Karga…

math.CV2017

Notes on the starlike log--harmonic mappings of order alpha

Rahim Kargar, Hesam Mahzoon

Let $h$ and $g$ be two analytic functions in the unit disc $Δ$ that $g (0) = 1$ . Also let $β$ be a complex number with $Re {β} > - 1/2$ . A function $f$ is said to be log--harmonic…

Characterizations of extremal hyperbolic rates via Herglotz measures and Koenigs linearization

Variable exponent modulus in symmetric domains

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

On Harnack inequality and harmonic Schwarz lemma

Intrinsic metrics defined with arithmetic and logarithmic mean values

Conformally invariant metrics and lack of Hölder continuity

Formulas for the visual angle metric

Landen transformations applied to approximation

Intrinsic metrics in polygonal domains

On quasiconformal close-to-convex harmonic mappings involving starlike functions

Notes on the norm of pre-Schwarzian derivatives on bi-univalent functions of order α

A note on the paper "Tang et al. [Bull Iran Math Soc (2019) doi:10.1007/s41980-019-00262-y]"

Notes on the norm of pre-Schwarzian derivatives of certain analytic functions

On certain subclasses of close-to-convex functions related with the second-order differential subordination

Further results for a subclass of univalent functions related with differential equation

On starlike functions related with the convex conic domain

On a certain subclass of strongly starlike functions

Some new inequalities for univalent functions

Some applications of differential subordination for certain starlike functions

On logarithmic coefficients of certain starlike functions related to the vertical strip

Volterra type integral operator and analytic function spaces

Some inequalities for a certain subclass of starlike functions

Further results for starlike functions related with Booth lemniscate

Notes on the starlike log--harmonic mappings of order alpha

Notes on the norm of pre-Schwarzian derivatives on bi-univalent functions of order $α$