• Kyungpook Mathematical Journal
• /
• v.57 no.4
• /
• pp.613-621
• /
• 2017

In this paper, we have constructed subclasses of bi-univalent functions associated with ${\lambda}$-bi-pseudo-starlike functions in the unit disc U. Furthermore we established bound on the coefficients for the subclasses $S^{\lambda}_{\Sigma}(k,{\alpha})$ and $S^{\lambda}_{\Sigma}(k,{\beta})$.

• Kyungpook Mathematical Journal
• /
• v.56 no.2
• /
• pp.597-610
• /
• 2016

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.4
• /
• pp.1377-1387
• /
• 2013

Let $f$ be a harmonic mapping on the unit disc ${\Delta}$ in $\mathbb{C}$. We give some condition for $f$ to be a quasiconformal homeomorphism on ${\Delta}$ and to have a quasiconformal extension to the whole plane $\bar{\mathbb{C}}$. We also obtain quasiconformal extension results for starlike harmonic mappings of order ${\alpha}{\in}(0,1)$.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.165-173
• /
• 2018

In this paper we obtain the bounds of the third Hankel determinants for the classes $\mathcal{S}^*({\alpha})$ of starlike functions of order ${\alpha}$ and $\mathcal{K}({\alpha}$) of convex functions of order ${\alpha}$. Moreover,we derive the sharp bounds for functions in these classes which are additionally 2-fold or 3-fold symmetric.

• Kyungpook Mathematical Journal
• /
• v.45 no.1
• /
• pp.123-130
• /
• 2005

In this paper we discuss a class of analytic functions related to the starlike functions in the unit disk. We prove that this class belongs to the class of close-to-convex functions, we obtain the sharp coefficient upper bounds and distortion theorem of this class, we also get the convexity radius of this class.

• 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.

• East Asian mathematical journal
• /
• v.17 no.2
• /
• pp.175-183
• /
• 2001

The main object of this paper is to investigate several majorization problems involving two subclasses $S_{p,q}(\gamma)$ and $C_{p,q}(\gamma)$ of p-valently starlike and p-valently convex functions of complex order ${\gamma}{\neq}0$ in the open unit disk $\mathbb{u}$. Relevant connections of the results presented here with those given by earlier workers on the subject are also indicated.

• Kyungpook Mathematical Journal
• /
• v.56 no.1
• /
• pp.147-159
• /
• 2016

In this paper, we obtained some properties for subclasses of starlike functions defined by convolution such as partial sums, integral means, square root and integral transform for these classes.

• 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.

• 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.