• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.77-85
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• 2011

In this paper, we introduce the integral operator $I_{\beta}$($p_1$, ${\ldots}$, $p_n$; ${\alpha}_1$, ${\ldots}$, ${\alpha}_n$)(z) analytic functions with positive real part. The radius of convexity of this integral operator when ${\beta}$ = 1 is determined. In particular, we get the radius of starlikeness and convexity of the analytic functions with Re {f(z)/z} > 0 and Re {f'(z)} > 0. Furthermore, we derive sufficient condition for the integral operator $I_{\beta}$($p_1$, ${\ldots}$, $p_n$; ${\alpha}_1$, ${\ldots}$, ${\alpha}_n$)(z) to be analytic and univalent in the open unit disc, which leads to univalency of the operators $\int\limits_0^z(f(t)/t)^{\alpha}$dt and $\int\limits_0^z(f'(t))^{\alpha}dt$.

• Kyungpook Mathematical Journal
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• 제46권4호
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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.

• 호남수학학술지
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• 제39권4호
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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.

• 호남수학학술지
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• 제39권2호
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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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• 제24권4호
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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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• 제59권3호
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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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• 제28권1호
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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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• 제53권4호
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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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• 제30권2호
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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.

• 대한수학회보
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• 제42권3호
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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$_{H}$($\alpha$, $\beta$).