• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.543-552
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• 2006

The purpose of the present paper is to introduce two novel subclasses $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$ and $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, starlikenes, and convexity for the functions belonging to the class $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$. These results are then appropriately applied to derive similar geometrical properties for the other class $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.591-601
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• 2017

In this paper, by means of the $S{\breve{a}}l{\breve{a}}gean$ operator, we introduce a new subclass $\mathcal{B}^{m,n}_{\Sigma}({\gamma};{\varphi})$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$. For functions belonging to this class, we consider Fekete-$Szeg{\ddot{o}}$ inequalities.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.233-245
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• 2017

In the present paper we introduce and investigate an interesting subclass ${\mathcal{K}}^{(k)}_s({\gamma},p) $ of analytic and p-valently close-to-convex functions in the open unit disk ${\mathbb{U}}$. For functions belonging to this class, we derive several properties as the inclusion relationships and distortion theorems. The various results presented here would generalize many known recent results.

• East Asian mathematical journal
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• v.24 no.4
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• pp.347-358
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• 2008

In this paper we investigate integral means inequalities for the integral operators $Q_{\lambda}^{\mu}$ and $P_{\lambda}^{\mu}$ applied to suitably normalized analytic functions. Further, we obtain some neighborhood and inclusion properties for a class of functions $G{\alpha}({\phi}, {\psi})$ (defined below). Several corollaries exhibiting the applications of the main results are considered in the concluding section.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.493-503
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• 2019

In the present investigation, we define two new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination in the open unit disk U. Furthermore, for functions in each of the subclasses introduced here, we establish upper bounds for the initial coefficients ${\mid}a_{m+1}{\mid}$ and ${\mid}a_{2m+1}{\mid}$. Also, we indicate certain special cases for our results.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.149-157
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• 2020

Some basic properties in connection with generalized relative order and generalized relative lower order of analytic functions in the unit disc have been dicussed in this article.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.615-624
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• 2013

The object of the present paper is to investigate the majorization properties of certain subclasses of analytic p-valent functions defined by convolution.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.351-360
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• 2022

In this paper, we will introduce the class of analytic functions called 𝓡 (𝛼, λ) and explore the different 5properties of the functions belonging to this class.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.563-569
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• 2005

In [2], Jahangiri studied the harmonic starlike functions of order $\alpha$, and he defined the class T$_{H}$($\alpha$) consisting of functions J = h + $\bar{g}$ where hand g are the analytic and the co-analytic part of the function f, respectively. In this paper, we introduce the class T$_{H}$($\alpha$, $\beta$) of analytic functions and prove various coefficient inequalities, growth and distortion theorems, radius of convexity for the function h, if the function J belongs to the classes T$_{H}$($\alpha$) and T$_{H}$($\alpha$, $\beta$).

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.671-684
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• 2021

The tenacity of the current paper is to find connections between various subclasses of analytic univalent functions by applying certain convolution operator involving generalized hypergeometric distribution series. To be more specific, we examine such connections with the classes of analytic univalent functions k - 𝓤𝓒𝓥^* (𝛽), k - 𝓢^*_p (𝛽), 𝓡 (𝛽), 𝓡^𝜏 (A, B), k - 𝓟𝓤𝓒𝓥^* (𝛽) and k - 𝓟𝓢^*_p (𝛽) in the open unit disc 𝕌.