Connecting quantum calculus and harmonic starlike functions

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On Harmonic Uniformly Starlike Functions Defined by an Integral Operator

Using the integral operator, we define and study a generalized family of complex-valued harmonic functions that are univalent, sense-preserving and are associated with uniformly harmonic functions in the unit disk. We obtain coefficient inequalities, extreme points and distortion bounds for the functions in our class. The results obtained for the our class reduce to the corresponding results fo...

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On Uniformly Starlike Functions

These are normalized functions regular and univalent in E: IzI < 1, for which f( E) is starlike with respect to the origin. Let y be a circle contained in E and let [ be the center of y. The Pinchuk question is this: Iff(z) is in ST, is it true thatf(y) is a closed curve that is starlike with respect tof(i)? In Section 5 we will see that the answer is no. There seems to be no reason to demand t...

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ژورنال

عنوان ژورنال: Filomat

سال: 2020

ISSN: 0354-5180,2406-0933

DOI: 10.2298/fil2005431a