Search arXiv⌕ Search

arXiv subjects

Mohsan Raza

Publications and source records attributed to Mohsan Raza.

5 recordsLinked to original sources
arXiv2026

On the Moduli Difference of Initial Logarithmic and Inverse Logarithmic Coefficients of Ma-Minda Convex Functions

Let $\mathcal{C}(Φ)$ denote a subclass of class $ \mathcal{C}$ of convex functions in the unit disc $\mathbb{D}=\{z:|z|<1, z\in \mathbb{C}\}$ defined by \begin{equation*} {Re}\left \{1+ \frac{ zf^{\prime \prime}(z)}{f^{\prime}(z)}\right \} \prec Φ(z), \end{equation*} where $Φ$ represents the Ma--Minda function in $\mathbb{D}$. For $f\in\mathcal{C}(Φ)$, we find the sharp estimates of $||γ_{2}|-|γ_{1}||$, where $γ_{1}$ and $γ_{2}$ are the first two logarithmic coefficients of $f$. The bound is also obtained for the inverse logarithmic coefficients $Γ_{1}$ and $Γ_{2}$. We then show that, under suitable conditions, the bounds for $||γ_{2}|-|γ_{1}||$ and $||Γ_{2}|-|Γ_{1}||$ are identical, which gives the invariance result between these functionals. We also present bounds for the differences for various classes of univalent functions by choosing particular function $Φ$. Thus our results unify several results studied in the literature.

math.CV↗
arXiv2026

Invariance of the Initial Coefficient Differences of Ma-Minda Convex Functions

Let $Φ$ be a univalent function in $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$% , $Φ(\mathbb{D})$ is symmetric with respect to the real axis, starlike with respect to $Φ(0)=1$, and $Φ^{\prime }(0)>0$. Let $\mathcal{C}% (Φ)$ denote the class of Ma-Minda convex functions. In this article, we present the bounds on $||a_{3}|-|a_{2}||$ for Taylor's coefficients of the function $f$ in the class $\mathcal{C}(Φ)$. We also establish the same bounds for the inverse coefficients. All the bounds we study here are sharp. We also present the conditions such that the bounds on $|a_{3}|-|a_{2}||$ and $|A_{3}|-|A_{2}||$ are invariant, where $A_{2}$ and $A_{3}$ are the first two coefficients of the Taylor series of the inverse functions of $f\in \mathcal{C}(Φ).$ Thus provides examples of invariance and nonvariance among the subclasses of convex functions.

math.CV↗
arXiv2025

The Third Hankel determinant for inverse coefficients of bounded turning functions

In this paper, we obtain sharp bounds for the third Hankel determinants of the coefficients of the inverse of bounded turning functions. Thus answering a negatively to a conjecture recently posed regarding these functions. Additionally, we offer a positive response for the Hankel determinant related to a class of bounded turning functions.

math.CV↗