Fekete-Szego and Zalcman Functional Estimates for Subclasses of Alpha-Convex Functions Related to Trigonometric Functions
Krishnan Marimuthu,
Uma Jayaraman,
TEODOR BULBOACA
Abstract:In this study we introduce the new classes $\mathcal{M}_{\alpha}(\sin)$ and $\mathcal{M}_{\alpha}(\cos)$ of $\alpha$-convex functions associated with sine and cosine functions. Also, we obtain the initial coefficient bounds for the first five coefficients of the functions that belong to these classes. Further, we determine the upper bound of Zalcman functional for the class $\mathcal{M}_{\alpha}(\cos)$ for the case $n=3$, showing that the Zalcman conjecture holds for this value. Moreover, the problem of the Fe… Show more
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