Abstract
We define and investigate a new subclass of Bazilevič type harmonic univalent functions using a linear operator. We investigated the harmonic structures in terms of its coefficient conditions, extreme points, distortion bounds, convolution, and convex combination. So, also, we discussed the subordination properties for the functions in this class.
Highlights
Let A denote the usual class of analytic functions of the form
We denote the subclass of A consisting of analytic and univalent functions f(z) in the unit disk U by S
If p is analytic in U and satisfies the differential subordination Φ(p(z), zp(z)) ≺ φ(z), p is called a solution of the differential subordination
Summary
We denote the subclass of A consisting of analytic and univalent functions f(z) in the unit disk U by S. We recall some definitions and concepts of classes of analytic functions. This class is called starlike class of analytic function. This class is called convex class of analytic function. If p is analytic in U and satisfies the differential subordination Φ(p(z), zp(z)) ≺ φ(z), p is called a solution of the differential subordination. The univalent function q is called a dominant of the solution of the differential subordination, p ≺ q. An analytic function q is called subordinate of the solution of the differential superordination if q ≺ p. For details (see [5,6,7])
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