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

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.571-582
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• 1998

The object of the present paper is to derive some sufficient conditions for p-valently close-to-convexity, p-valently starlikeness and p-valently convexity.

• 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.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.305-315
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• 1995

The class $R_{\gamma-1,p}(A,B,\alpha)$ for $-1 \leq B < A \leq 1,\gamma > (B -1)p+(A_B)(p-\alpha)/1-B$ and $0 \leq \alpha < p$ consisting of p-valently analytic functions in the open unit disc is defined with the help of convolution technique. We study containment property, integral transforms and a sufficient condition for an analytic function to be in $R_{\gamma-1,p}(A,B,\alpha)$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1805-1818
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• 2015

In this article, we first consider a linear multiplier fractional q-differintegral operator and then use it to define new subclasses of p-valent analytic functions in the open unit disk U. An attempt has also been made to obtain two new q-integral operators and study their sufficient conditions on some classes of analytic functions. We also point out that the operators and classes presented here, being of general character, are easily reducible to yield many diverse new and known operators and function classes.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.867-876
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• 2016

The object of the present paper is to investigate the starlikeness of the class of functions $f(z)=z^p+{\sum\limits_{k=n}^{\infty}}a_p+k^{z^{p^{+k}}} (p,n{\in}{\mathbb{N}}=\{1,2,{\ldots}\})$ which are analytic and p-valent in the unit disc U and satisfy the condition $\|(1-{\lambda}({\frac{f(z)}{z^p}})^{\alpha}+{\lambda}{\frac{zf^{\prime}(z)}{pf(z)}}({\frac{f(z)}{z^p}})^{\alpha}-1\|$ < ${\mu}$ (0 < ${\mu}{\leq}1$, ${\lambda}{\geq}0$, ${\alpha}$ > 0, $z{\in}U$). The starlikeness of certain integral operator are also discussed. The results obtained generalize the related works of some authors and some other new results are also obtained.