Miskolc Mathematical Notes
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: https://doi.org/10.18514/MMN.2019.2405


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