Hankel Determinant Problem for q-strongly Close-to-Convex Functions

  • Khalida Inayat Noor Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
  • Muhammad Aslam Noor Mathematics Department, COMSATS University Islamabad, Islamabad, Pakistan
Keywords: q-derivative, convolution operator, starlike functions, close-to-convex functions, Hankel determinant

Abstract

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:
$$D_qf(z)= \frac{f(z)-f(qz)}{(1-q)z}, \quad z\neq0\quad D_qf(0)= f^{\prime}(0). $$
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.

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Published
2022-01-11
How to Cite
Noor, K. I., & Noor, M. A. (2022). Hankel Determinant Problem for q-strongly Close-to-Convex Functions. Earthline Journal of Mathematical Sciences, 8(2), 227-236. https://doi.org/10.34198/ejms.8222.227236
Section
Articles