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Kamaljeet Gangania

Publications and source records attributed to Kamaljeet Gangania.

15 recordsLinked to original sources
arXiv2022

Geometric Properties of Functions Containing Derivatives of Bessel Functions

In this paper our aim is to find the radii of $γ$-Spirallike of order $α$ and convex $γ$-Spirallike of order $α$ for three different kinds of normalizations of the function $N_ν(z)=az^2J_ν^{\prime\prime}(z)+bzJ_ν^{\prime}(z)+cJ_ν(z),$ where $J_ν(z)$ is the Bessel function of the first kind of order $ν.$ Moreover, the $\mathcal{S}^*\left(φ\right)-$radii and $\mathcal{C}\left(φ\right)-$radii of these normalized functions are investigated. The tables are created and visual verification with graphs are made by giving special values to the real numbers $a,$ $b$ and $c$ in the obtained results.

math.CV↗
arXiv2022

Theory of certain Non-Univalent Analytic functions

We investigate the non-univalent function's properties reminiscent of the theory of univalent starlike functions. Let the analytic function $ψ(z)=\sum_{i=1}^{\infty}A_i z^i$, $A_1\neq0$ be univalent in the unit disk. Non-univalent functions may be found in the class $\mathcal{F}(ψ)$ of analytic functions $f$ of the form $f(z)=z+\sum_{k=2}^{\infty}a_k z^k$ satisfying $({zf'(z)}/{f(z)}-1) \prec ψ(z)$. Such functions, like the Ma and Minda classes of starlike functions, also have nice geometric properties. For these functions, growth and distortion theorems have been established. Further, we obtain bounds for some sharp coefficient functionals and establish the Bohr and Rogosinki phenomenon for the class $\mathcal{F}(ψ)$. Non-analytic functions that share properties of analytic functions are known as Poly-analytic functions. Moreover, we compute Bohr and Rogosinski's radius for Poly-analytic functions with analytic counterparts in the class $\mathcal{F}(ψ)$ or classes of Ma-Minda starlike and convex functions.

math.CV↗
arXiv2022

Radius Properties of Harmonic Mappings with Fixed Analytic Part

We investigate harmonic mappings $f=h+\bar{g}$ defined in the unit disk, where $g$ and $h$ satisfy certain prescribed conditions and the analytic part $h$ belongs to the Ma and Minda class of starlike functions. Certain sharp radius results for univalency, close-to-convexity, fully starlikeness, fully convexity, and radius of strongly starlikeness are established. We also calculate the radius of uniformly starlikeness and convexity for these functions. Several results enhance the well-known radius results.

math.CV↗
arXiv2022

Radii problems for Ma-Minda Starlikeness

For the standard Ma-Minda class $\mathcal{S}^{*}(ψ)$ of univalent starlike functions, we derive $\mathcal{S}^{*}(ψ)$-radii for some well-known special functions. In addition, we obtain the set of extremal functions for the classical problem $$\max_{f\in \mathcal{S}^{*}(ψ)}^{}\left|Φ\left(\log{(f(z)/z)}\right)\right| \quad \text{or} \quad \max_{f\in \mathcal{S}^{*}(ψ)}^{}\ReΦ\left(\log{(f(z)/z)}\right),$$ where $Φ$ is a non-constant entire function. Moreover, we prove certain results on convolution and radius estimates for the case when $ψ(\mathbb{D})$ is starlike.

math.CV↗
arXiv2022

A generalized Bohr-Rogosinski phenomenon

In this paper, we generalize the Bohr-Rogosinski sum for the Ma-Minda classes of starlike and convex functions. Also the phenomenon is studied for the classes of starlike functions with respect to symmetric points and conjugate points along with their convex cases. Further, the connection between the derived results and the known ones are established with the suitable examples.

math.CV↗
arXiv2021

Bohr Phenomenon for $K$-Quasiconformal harmonic mappings and Logarithmic Power Series

In this article, we establish the Bohr inequalities for the sense-preserving $K$-quasiconformal harmonic mappings defined in the unit disk $\mathbb{D}$ involving classes of Ma-Minda starlike and convex univalent functions, usually denoted by $\mathcal{S}^*(ψ)$ and $\mathcal{C}(ψ)$ respectively, and for $\log (f(z)/z)$ where $f$ belongs to the Ma-Minda classes or satisfies certain differential subordination. We also estimate Logarithmic coefficient's bounds for the functions in $\mathcal{C}(ψ)$ for the case $ψ(\mathbb{D})$ be convex.

math.CV↗
arXiv2021

On certain Generalizations of $\mathcal{S}^*(ψ)$: II

In this paper, we prove various radius results and obtain sufficient conditions using the convolution for the Ma-Minda classes $\mathcal{S}^*(ψ)$ and $\mathcal{C}(ψ)$ of starlike and convex analytic functions. We also obtain the Bohr radius for the class $ S_{f}(ψ):= \{g(z)=\sum_{k=1}^{\infty}b_k z^k : g \prec f \}$ of subordinants, where $f\in \mathcal{S}^*(ψ).$ The results are improvements and generalizations of several well known results.

math.CV↗
arXiv2021

Bohr-Rogosinski phenomenon for $\mathcal{S}^*(ψ)$ and $\mathcal{C}(ψ)$

In Geometric function theory, occasionally attempts have been made to solve a particular problem for the Ma-Minda classes, $\mathcal{S}^*(ψ)$ and $\mathcal{C}(ψ)$ of univalent starlike and convex functions, respectively. Recently, a popular radius problem generally known as Bohr's phenomenon has been studied in various settings, however little is known about Rogosinski radius. In this article, for a fixed $f\in \mathcal{S}^*(ψ)$ or $\mathcal{C}(ψ),$ the class of analytic subordinants $S_{f}(ψ):= \{g : g\prec f \} $ is studied for the Bohr-Rogosinski phenomenon in a general setting. It's applications to the classes $\mathcal{S}^*(ψ)$ and $\mathcal{C}(ψ)$ are also shown.

math.CV↗
arXiv2020

On Certain Generalizations of $\mathcal{S}^*(ψ)$

We deal with different kinds of generalizations of $\mathcal{S}^*(ψ)$, the class of Ma-Minda starlike functions, in addition to a majorization result of $\mathcal{C}(ψ),$ the class of Ma-Minda convex functions, which are enlisted as follows: 1. Let $h$ be an analytic function, $f$ be in $\mathcal{C}(ψ)$ and $h$ be majorized by $f$ in the unit disk $\mathbb{D},$ then for a given $ψ,$ we derive a general equation, which yields the radius constant $r_ψ$ such that $|h'(z)|\leq |f'(z)|$ in $|z|\leq r_ψ$. Consequently, obtain results associating $\mathcal{S}^*(ψ)$ and others. 2. We find the largest radius $r_0$ so that the product function $g(z)h(z)/z$ belongs to a desired class for $|z|<r_0$ whenever $g\in \mathcal{S}^*(ψ_1)$ and $h\in \mathcal{S}^*(ψ_2).$ Also we obtain a condition for the functions to be in $\mathcal{S}^*(ψ)$ 3. We obtain the modified distortion theorem for $\mathcal{S}^*(ψ)$ with a general perspective. 4. For a fixed $f\in \mathcal{S}^*(ψ),$ the class of subordinants $S_{f}(ψ):= \{g : g\prec f \} $ is introduced and studied for the Bohr-phenomenon and a couple of conjectures are also proposed.

math.CV↗
arXiv2020

Bohr radius for some classes of Harmonic mappings

We introduce a general class of sense-preserving harmonic mappings defined as follows: \begin{equation*} \mathcal{S}^0_{h+\bar{g}}(M):= \{f=h+\bar{g}: \sum_{m=2}^{\infty}(γ_m|a_m|+δ_m|b_m|)\leq M, \; M>0 \}, \end{equation*} where $h(z)=z+\sum_{m=2}^{\infty}a_mz^m$, $g(z)=\sum_{m=2}^{\infty}b_m z^m$ are analytic functions in $\mathbb{D}:=\{z\in\mathbb{C}: |z|\leq1 \}$ and \begin{equation*} γ_m,\; δ_m \geq α_2:=\min \{γ_2, δ_2\}>0, \end{equation*} for all $m\geq2$. We obtain Growth Theorem, Covering Theorem and derive the Bohr radius for the class $\mathcal{S}^0_{h+\bar{g}}(M)$. As an application of our results, we obtain the Bohr radius for many classes of harmonic univalent functions and some classes of univalent functions.

math.CV↗
arXiv2020

On Geometrical Properties of Certain Analytic functions

We introduce the class of analytic functions $$\mathcal{F}(ψ):= \left\{f\in \mathcal{A}: \left(\frac{zf'(z)}{f(z)}-1\right) \prec ψ(z),\; ψ(0)=0 \right\},$$ where $ψ$ is univalent and establish the growth theorem with some geometric conditions on $ψ$ and obtain the Koebe domain with some related sharp inequalities. Note that functions in this class may not be univalent. As an application, we obtain the growth theorem for the complete range of $α$ and $β$ for the functions in the classes $\mathcal{BS}(α):= \{f\in \mathcal{A} : ({zf'(z)}/{f(z)})-1 \prec {z}/{(1-αz^2)},\; α\in [0,1) \}$ and $\mathcal{S}_{cs}(β):= \{f\in \mathcal{A} : ({zf'(z)}/{f(z)})-1 \prec {z}/({(1-z)(1+βz)}),\; β\in [0,1) \}$, respectively which improves the earlier known bounds. The sharp Bohr-radii for the classes $S(\mathcal{BS}(α))$ and $\mathcal{BS}(α)$ are also obtained. A few examples as well as certain newly defined classes on the basis of geometry are also discussed.

math.CV↗
arXiv2020

$\mathcal{S}^{*}(ϕ)$ and $\mathcal{C}(ϕ)$-radii for some special functions

In this paper, we consider the Ma-Minda classes of analytic functions $\mathcal{S}^{*}(ϕ):= \{f\in \mathcal{A} : ({zf'(z)}/{f(z)}) \prec ϕ(z) \}$ and $\mathcal{C}(ϕ):= \{f\in \mathcal{A} : (1+{zf''(z)}/{f'(z)}) \prec ϕ(z) \}$ defined on the unit disk $\mathbb{D}$ and show that the classes $\mathcal{S}^{*}(1+αz)$ and $\mathcal{C}(1+αz)$, $0<α\leq 1$ solve the problem of finding the sharp $\mathcal{S}^{*}(ϕ)$-radii and $\mathcal{C}(ϕ)$-radii for some normalized special functions, whenever $ϕ(-1)=1-α$. Radius of strongly starlikeness is also considered.

math.CV↗
arXiv2020

A Cardioid Domain and Starlike Functions

We introduce and study a class of starlike functions defined by \begin{equation*} \mathscr{S}^*_\wp:=\left\{f\in\mathcal{A}: \frac{zf'(z)}{f(z)}\prec 1+ze^z=:\wp(z)\right\}, \end{equation*} where $\wp$ maps the unit disk onto a cardioid domain. We find the radius of convexity of $\wp(z)$ and establish the inclusion relations between the class $ \mathscr{S}^*_\wp$ and some well-known classes. Further we derive sharp radius constants and coefficient related results for the class $ \mathscr{S}^*_\wp$.

math.CV↗