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

By Hari M. Srivastava, Adela O. Mostafa, Mohamed Kamal Aouf, Hanaa M. Zayed. Miskolc Mathematical Notes, 2019

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In this paper, we introduce and study some subclasses of p-valently analytic functions in the open unit disk 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 fakg1kDpC1 of each of these subclasses of p-valently analytic functions, we derive sharp bounds for the Fekete-Szegő functional given by ˇ̌̌ apC2 a 2 pC1 ˇ̌̌ : Relevant connections of the results presented in this paper with those derived in earlier works are also considered. 2010 Mathematics Subject Classification: 26A33; 33C20; 30C45; 30C50

Subfields: Geometry and Topology, Pharmacology

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