• Korean Journal of Mathematics
• /
• v.31 no.3
• /
• pp.243-258
• /
• 2023

A normalized analytic function f defined on the unit disk 𝔻 is starlike of reciprocal order α, 0 ≤ α < 1, if Re(f(z)/(zf'(z))) > α for all z ∈ 𝔻. Such functions are starlike and therefore univalent in 𝔻. Using the well-known Miller-Mocanu differential subordination theory, sufficient conditions involving differential inclusions are obtained for a normalized analytic function to be starlike of reciprocal order α. Furthermore, a few conditions are derived for a function f to belong to a subclass of reciprocal starlike functions, satisfying |f(z)/(zf'(z)) - 1| < 1 - α.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.697-704
• /
• 2011

By using the method of differential subordinations, we derive some sufficient conditions for strongly starlike functions associated with a linear operator. All these results presented here are sharp.

• Honam Mathematical Journal
• /
• v.46 no.1
• /
• pp.120-135
• /
• 2024

A normalized analytic function f, defined on the unit disk 𝔻, is starlike of reciprocal order α > 1 if the real part of f(z)/(zf'(z)) is less than α for all z ∈ 𝔻. By utilizing the theory of differential subordination, we establish several sufficient conditions for analytic functions defined on 𝔻 to be starlike of reciprocal order. Additionally, we investigate the conditions under which the function f(z)/(zf'(z)) is subordinate to the function 1 + (α - 1)z. This subordination, in turn, is sufficient for the function f to be starlike of reciprocal order α > 1.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.993-1010
• /
• 2022

In this paper, we establish some radius results and inclusion relations for starlike functions associated with a petal-shaped domain.

• Journal of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.331-357
• /
• 2020

Let p be an analytic function defined on the open unit disk 𝔻. We obtain certain differential subordination implications such as ψ(p) := p^λ(z)(α+βp(z)+γ/p(z)+δzp'(z)/p^j(z)) ≺ h(z) (j = 1, 2) implies p ≺ q, where h is given by ψ(q) and q belongs to 𝒫, by finding the conditions on α, β, γ, δ and λ. Further as an application of our derived results, we obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy |log(zf'(z)/f(z))| < 1, |(zf'(z)/f(z))² - 1| < 1 and zf'(z)/f(z) lying in the parabolic region v² < 2u - 1.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.1
• /
• pp.71-81
• /
• 2021

The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.

• Honam Mathematical Journal
• /
• v.43 no.4
• /
• pp.627-639
• /
• 2021

Numerical techniques are used to determine the radius of convexity of the starlike functions related to cardioid shaped bounded domain. In addition, radius constants of certain starlikeness associated with right half plane of various starlike functions are computed.

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.4
• /
• pp.615-620
• /
• 2008

For analytic functions f(z) in the open unit disc $\mathbb{D}$, an operator $N_{\alpha}(f(z))$ relating with starlike functions is introduced. The object of the present paper is to discuss some properties of the operator $N_{\alpha}(f(z))$.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.291-301
• /
• 2000

We give sufficient coefficient conditions for a class of meromorphic univalent harmonic functions that are starlike of some order. Furthermore, it is shown that these conditions are also necessary when the coefficients of the analytic part of the function are positive and the coefficients of the co-analytic part of the function are negative. Extreme points, convolution and convex combination conditions for these classes are also determined. Fianlly, comparable results are given for the convex analogue.

• Kyungpook Mathematical Journal
• /
• v.58 no.2
• /
• pp.257-270
• /
• 2018

The well-known theory of differential subordination developed by Miller and Mocanu is applied to obtain several inclusions between $Carath{\acute{e}}odory$ functions and starlike functions. These inclusions provide sufficient conditions for normalized analytic functions to belong to certain class of Ma-Minda starlike functions.