TY - JOUR
AU - Khalida Inayat Noor
AU - Muhammad Aslam Noor
PY - 2022/01/11
Y2 - 2022/05/19
TI - Hankel Determinant Problem for q-strongly Close-to-Convex Functions
JF - Earthline Journal of Mathematical Sciences
JA - EJMS
VL - 8
IS - 2
SE - Articles
DO - 10.34198/ejms.8222.227236
UR - https://earthlinepublishers.com/index.php/ejms/article/view/449
AB - In this paper, we introduce a new class $K_{q}(\alpha), \quad 0<\alpha \leq1, \quad 0<q<1, $ of normalized analytic functions $f $ such that $\big|\arg\frac{D_qf(z)}{D_qg(z)}\big| \leq \alpha \frac{\pi}{2},$ where $g$ is convex univalent in $E= \{z: |z|<1\} $ and $D_qf $ is the $q$-derivative of $f $ defined as:$$D_qf(z)= \frac{f(z)-f(qz)}{(1-q)z}, \quad z
eq0\quad D_qf(0)= f^{\prime}(0). $$The problem of growth of the Hankel determinant $H_n(k) $ for the class $K_q(\alpha) $ is investigated. Some known interesting results are pointed out as applications of the main results.
ER -