• The Pure and Applied Mathematics
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• v.10 no.1
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• pp.1-11
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• 2003

In this paper we derive some sufficient conditions for starlikeness and close-to-convexity of order ${\alpha}$ of meromorphic functions in the punctured unit disk.

• East Asian mathematical journal
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• v.21 no.2
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• pp.219-231
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• 2005

This paper investigates some results (Theorems 2.1-2.3, below) concerning certain classes of analytic and univalent functions, involving the familiar fractional derivative operators. We state interesting consequences arising from the main results by mentioning the cases connected with the starlikeness, convexity, close-to-convexity and quasi-convexity of geometric function theory. Relevant connections with known results are also emphasized briefly.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.719-731
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• 2020

In this article, we find some sufficient conditions under which the modified Lommel function is close-to-convex with respect to - log(1 - z) and ${\frac{1}{2}}\;{\log}\;\({\frac{1+z}{1-z}}\)$. Starlikeness, convexity and uniformly close-to-convexity of the modified Lommel function are also discussed. Some results related to the H. Silverman are also the part of our investigation.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.331-347
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• 2017

The aim of the present paper is to introduce a new subclass of meromorphic functions with positive coefficients defined by a certain integral operator and a necessary and sufficient condition for a function f to be in this class. We obtain coefficient inequality, meromorphically radii of close-to-convexity, starlikeness and convexity, convex linear combinations, Hadamard product and integral transformation for the functions f in this class.

• 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.

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

• Honam Mathematical Journal
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• v.41 no.1
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• pp.101-116
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• 2019

In this paper our aim is to establish some geometric properties (like starlikeness, convexity and close-to-convexity) for the generalized and normalized Dini functions. In order to prove our main results, we use some inequalities for ratio of these functions in normalized form and classical result of Fejer.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.949-965
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• 2021

The main focus of the present paper is to present new set of sufficient conditions so that the normalized form of the Mittag-Leffler and Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disk. Interesting consequences and examples are derived to support that these results are better than the existing ones and improve several results available in the literature.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1035-1046
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• 2015

In this work we present some geometric properties (like star-likeness and convexity of order ${\alpha}$ and also close-to-convexity of order ($1+{\alpha}$)/2) for normalized of Lommel functions of the first kind. In order to prove our main results, we use the technique of differential subordinations and some inequalities. Furthermore, we present some applications of convexity involving Lommel functions associated with the Hardy space of analytic functions, i.e., we obtain conditions for the function $h_{{\mu},{\upsilon}}(z)$ to belong to the Hardy space $H^p$.

• East Asian mathematical journal
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• v.25 no.1
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• pp.39-44
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• 2009

The aim of the present investigation is to give some criterion for certain multivalently analytic functions and (or) multivalently meromorphic functions in the corresponding domains.