English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

For $\alpha\in(\pi, \pi]$, let $\mathcal{R}_\alpha(\phi)$ denote the class of all normalized analytic functions in the open unit disk $\mathbb{U}$ satisfying the following differential subordination: $$f'(z)+\frac{1}{2}\left(1+e^{i\alpha}\right)zf''(z)\prec\phi(z)\qquad (z\in\mathbb{U}),$$ where the function $\phi(z)$ is analytic in the open unit disk $\mathbb{U}$ such that $\phi(0)=1$. In this paper, various integral and convolution characterizations, coefficient estimates and differential subordination results for functions belonging to the class $\mathcal{R}_\alpha(\phi)$ are investigated. The Fekete-Szeg\"{o} coefficient functional associated with the $k$th root transform $[f(z^k)]^{1/k}$ of functions in $\mathcal{R}_\alpha(\phi)$ is obtained. A similar problem for a corresponding class $\mathcal{R}_{\Sigma;\alpha}(\phi)$ of bi-univalent functions is also considered. Connections with previous known results are pointed out.

Certain subclass of analytic functions defined by means of differential subordination