arXiv subjects
Publications and source records attributed to Lokenath Thakur.
In this artcle, we introduce and investigate a subclass of Bazilevi{č} functions, denoted by $\mathcal{B}_{φ_{A,B}}(α^{(m)})$. We determine the Hardy space to which this subclass of Bazilevi{č} functions belong to. Additionally, we provide a necessary condition for a particular case of this subclass. Finally, we obtain a sharp coefficient estimate for the functions associated with $\mathcal{B}_1(α).$
In this paper, we investigate three specific subclasses of Ma-Minda type convex functions: namely, convex functions of order $α$, Janowski convex functions, and Robertson functions of normalized analytic functions defined in the open unit disk. For these classes, we establish logarithmic coefficient inequalities concerning both individual coefficient estimates and weighted series. The results presented here correct some earlier erroneous results and extend several previously known ones.
For $0\le α\le 1 $, let $\mathcal{BS}(α)$ be the class of all analytic functions in the unit disk $\mathbb{D}:=\{~z\in\mathbb{C}:|z|<1\}$ with normalization $f(0)=0$ and $f'(0)=1$ that satisfy the subordinate relation $zf'(z)/f(z)-1\prec z/(1-αz^2)$ and $\mathcal{BK}(α)$ be the class of all functions $f$ for which $zf' \in \mathcal{BS}(α)$. In this article, we obtain a sharp estimate of the initial Taylor coefficients and logarithmic coefficients for functions in the classes $\mathcal{BS}(α)$ and $\mathcal{BK}(α)$. Further, we obtain the radius of convexity and study the pre-Schwarzian norm for the classes $\mathcal{BS}(α)$ and $\mathcal{BK}(α)$.