• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.225-234
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• 2023

In this paper, we use the use the linear operator ʒ^x_τ,σ(u, v, y)𝔣(z) and the concept of the subordination to analyse the general class of all analytic univalent functions. Our main results are implication properties between the classes of such functions and the application of these properties to special cases.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1103-1114
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• 2023

The aim of the present paper is to obtain some mapping properties of subordinations by certain univalent functions in the open unit disk associated with a family of linear operators. Moreover, we also consider some applications for integral operators.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.705-714
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• 2015

In this paper, we introduce and investigate an interesting subclass $M_{\Sigma}({\gamma},{\lambda},{\delta},{\varphi})$ of analytic and bi-univalent functions of complex order in the open unit disk ${\mathbb{U}}$. For functions belonging to the class $M_{\Sigma}({\gamma},{\lambda},{\delta},{\varphi})$ we investigate the coefficient estimates on the first two Taylor-Maclaurin coefficients ${\mid}{\alpha}_2{\mid}$ and ${\mid}{\alpha}_3{\mid}$. The results presented in this paper would generalize and improve some recent works of [1],[5],[9].

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.677-688
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• 2018

In this paper, we introduce and investigate a new subclass of bi-univalent functions defined by $S{\breve{a}}l{\breve{a}}gean$ q-calculus operator in the open disk ${\mathbb{U}}$. For functions belonging to the subclass, we obtain estimates on the first two Taylor-Maclaurin coefficients ${\mid}a_2{\mid}$ and ${\mid}a_3{\mid}$. Some consequences of the main results are also observed.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.257-269
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• 2022

In the present paper, a subclass of analytic and bi-univalent functions is defined using a symmetric q-derivative operator by means of Gegenbauer polynomials. Coefficients bounds for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szegö problem for this subclass is solved. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.589-599
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• 2023

The object of this study is to introduce a new subclass of univalent analytic functions on the open unit disk. This subclass is created by utilizing univalent analytic functions with negative coefficients. We first explore the specific properties that functions in this subclass must possess before examining their coefficient characterization. By applying this approach, we observe several fascinating features, including coefficient approximations, growth and distortion theorems, extreme points and a demonstration of the radius of starlikeness and convexity for functions belonging to this subclass.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.95-106
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• 2009

A comprehensive class of starlike univalent functions defined by Dziok-Srivastava operator is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Further distortion bounds, extreme points and results on partial sums are investigated.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.679-688
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• 2015

In this paper, we obtain Fekete-$Szeg{\ddot{o}}$ inequalities for certain subclasses of analytic univalent functions of complex order associated with quasi-subordination.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.215-224
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• 2019

In the present paper, some generalizations of analytic functions have been considered and the bounds of the coefficients of these classes of bi-univalent functions have been investigated.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.781-794
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• 2020

In this article, we investigate the upper bounds on the coefficients for inverse of functions belongs to certain classes of univalent functions and in particular for the functions convex in one direction. Bounds on the Fekete-Szegö functional and third order Hankel determinant for these classes have also investigated.