MMN-2405
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
H. M. Srivastava; A. O. Mostafa; M. K. Aouf; H. M. Zayed;Abstract
In this paper, we introduce and study some subclasses of
$p$-valently analytic functions in the open unit disk
$\mathbb{U}$ by applying the $q$-derivative operator and the
fractional $q$-derivative operator in conjunction with the
principle of subordination between analytic functions.
For the Taylor-Maclaurin coefficients
$\{a_{k}\}_{k=p+1}^{\infty}$ of each of these
subclasses of $p$-valently analytic functions,
we derive sharp bounds for the Fekete-Szeg\"{o}
functional given by
$$\left\vert a_{p+2}-\mu a_{p+1}^{2}\right\vert.$$
Relevant connections of the results presented in this paper
with those derived in earlier works are also considered.
Vol. 20 (2019), No. 1, pp. 489-509
DOI: 10.18514/MMN.2019.2405