A generalization of starlike functions of order alpha

By Sarita Agrawal, S. Sahoo. 2014

94 citations recorded by the source corpus.

For every $q\in(0,1)$ and $0\le \alpha<1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $\alpha$, on the open unit disk. We study this class of functions and explore some inclusion properties with the well-known class of starlike functions of order $\alpha$. The paper is also devoted to the discussion on the Herglotz representation formula for analytic functions $zf'(z)/f(z)$ when $f(z)$ is $q$-starlike of order $\alpha$. As an application we also discuss the Bieberbach conjecture problem for the $q$-starlike functions of order $\alpha$. Further application includes the study of the order of $q$-starlikeness of the well-known basic hypergeometric functions introduced by Heine.

Subfields: Geometry and Topology, Polymers and Plastics

View Paper: https://www.semanticscholar.org/paper/1d3a3b10286c7154c19544ca139d80c42fe5b42f

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In Geometry and Topology

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Citations in the corpus

Some Applications of a New Integral Operator in q-Analog for Multivalent Functions (2019, methodology): “This theory was later extended to the family of q-starlike function with some order by Agrawal and Sahoo [5].”
On a generalization of starlike functions (2018, background): “Estimating coefficient of functions from the class of univalent functions and its subclasses is of interest among function theorists since last decade; see for instance [2, 4].”
Some general families of q-starlike functions associated with the Janowski functions (2019, methodology): “If we set k = 0, A = 1 − 2α (0 5 α < 1) and B = −1 in Definition 12, we obtain the class Sq (α) which was introduced and studied by Agrawal and Sahoo [1].”
The Faber polynomial expansion method and its application to the general coefficient problem for some subclasses of bi-univalent functions associated with a certain q-integral operator (2018, methodology): “Motivated by these and other recent works (see, for example, [1], [14] and [30]), here we make use of the q-analysis in order to define new subclasses of analytic and bi-univalent”
Basic and fractional q-calculus and associated Fekete-Szegő problem for p-valently q-starlike functions and p-valently q-convex functions of complex order (2019, background): “p;'/ of p-valently q-starlike functions of complex order b in U (see also [1]):”