Abstract
In this article, we determine certain conditions under which the partial sums involving thecomplex Baskakov-Stancu operators of analytic univalent functions of bounded turning are also of boundedturning. Moreover, we consider some geometric properties such as starlikeness and convexity for these partialsums. The lower bound of the partial sums of univalent functions is computed using the lower bound of thecomplex Baskakov-Stancu operators of analytic functions
Highlights
Concepts in geometric function theoryOne of the major branches of complex analysis is univalent function theory: the study of one-to-one analytic functions
It was shown that the partial sums of the Libera integral operator of univalent functions is starlike in |z|
[7], it was shown that the partial sums of the Libera integral operator of functions of bounded turning are of bounded turning
Summary
One of the major branches of complex analysis is univalent function theory: the study of one-to-one analytic functions. A domain E of the complex plane is said to be convex if and only if the line segment joining any two points of E lies entirely in E : An analytic, univalent function f in the unit disk U mapping the unit disk onto some convex domain is called a convex function. A function f (z) which is analytic and univalent in the unit disk U, f (0) = 0 and maps U onto a starlike domain with respect to the origin. A function f ∈ A is called starlike of order μ if it satisfies the following inequality. A function f ∈ A is called convex of order μ if it satisfies the following inequality zf ′′(z) f ′(z).
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