• Title, Summary, Keyword: subordination

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SOME SUBORDINATION PROPERTIES OF THE LINEAR OPERATOR

  • PANIGRAHI, TRAILOKYA
    • Journal of the Korean Mathematical Society
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    • v.53 no.1
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    • pp.147-159
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    • 2016
  • In this paper, subordination results of analytic function $f{\in}{\mathcal{A}}_p$ involving linear operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are obtained. By applying the differential subordination method, results are derived under some sufficient subordination conditions. On using some hypergeometric identities, corollaries of the main results are derived. Furthermore, convolution preserving properties for a class of multivalent analytic function associated with the operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are investigated.

SUBORDINATION RESULTS FOR CERTAIN SUBCLASSES BY USING INTEGRAL OPERATOR DEFINED IN THE SPACE OF ANALYTIC FUNCTIONS

  • Sakar, F. Muge;Guney, H. Ozlem
    • Honam Mathematical Journal
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    • v.40 no.2
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    • pp.315-323
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    • 2018
  • In this study, firstly we introduce generalized differential and integral operator, also using integral operator two classes are presented. Furthermore, some subordination results involving the Hadamard product (Convolution) for these subclasses of analytic function are proved. A number of consequences of some of these subordination results are also discussed.

SOME RESULTS ON CERTAIN CLASS OF ANALYTIC FUNCTIONS BASED ON DIFFERENTIAL SUBORDINATION

  • Prajapat, Jugal Kishore;Agarwal, Ritu
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.1-10
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    • 2013
  • In the present paper we derive various useful properties and characteristics for certain class of analytic functions by using the techniques of differential subordination. Some interesting corollaries and applications of the results presented here are also discussed.

Verbal Conjunctions in Korean, English and Japanese

  • Oh, Chisung
    • Cross-Cultural Studies
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    • v.32
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    • pp.109-132
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    • 2013
  • This paper compares sequential and non-sequential verbal conjunctions in Korean, English, and Japanese by looking at how sequential verbal conjunction is treated in each language. It frist reviews verbal conjunctions in Korean, where sequential conjunction is treated as subordination and non-sequential conjunction is treated as coordination, and looks at verbal conjunctions in English and Japanese to see whether or not sequential conjunction in those languages is subordination. According to Oh (2010), sequential and non-sequential conjunctions in Korean behave quite differently with respect to the tense and negation in the final conjunct. Also, Cho (1995, 2005) and Kwon (2004) show that syntactic operations such as extraction and scrambling clearly distinguish sequential conjunction from non-sequential conjunction. The purpose of this paper is to see how sequential and non-sequential conjunctions are analyzed in English and Japanese and to compare those languages with Korean, especially focusing on whether or not sequential conjunctions in English and Japanese are treated as subordination. For this purpose, I first investigate how tense and negation, which provided crucial evidence for concluding that Korean sequential conjunction is subordination, is interpreted in sequential and non-sequential verbal conjunctions in English and Japanese. Also, I investigate the syntactic properties of sequential and non-sequential conjunctions with respect to syntactic operations such as extraction and scrambling in those languages. The results of the investigation show that in Japanese, which is considered typologically similar to Korean, the sequential conjunction is a case of subordination, while in English, which is considered typologically different from Korean, both sequential and non-sequential conjunctions are treated as coordination.

A NOTE ON SEMI-SELFDECOMPOSABILITY AND OPERATOR SEMI-STABILITY IN SUBORDINATION

  • Choi, Gyeong-Suk;Kim, Yun-Kyong;Joo, Sang-Yeol
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.3
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    • pp.483-490
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    • 2010
  • Some results on inheritance of operator semi-selfdecomposability and its decreasing subclass property from subordinator to subordinated in subordination of a L$\acute{e}$evy process are given. A main result is an extension of results of [5] to semi-selfdecomposable subordinator. Its consequence is discussed.

Integral operators that preserve the subordination

  • Bulboaca, Teodor
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.627-636
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    • 1997
  • Let $H(U)$ be the space of all analytic functions in the unit disk $U$ and let $K \subset H(U)$. For the operator $A_{\beta,\gamma} : K \longrightarrow H(U)$ defined by $$ A_{\beta,\gamma}(f)(z) = [\frac{z^\gamma}{\beta + \gamma} \int_{0}^{z} f^\beta (t)t^{\gamma-1} dt]^{1/\beta} $$ and $\beta,\gamma \in C$, we determined conditions on g(z), $\beta and \gamma$ such that $$ z[\frac{z}{f(z)]^\beta \prec z[\frac{z}{g(z)]^\beta implies z[\frac{z}{A_{\beta,\gamma}(f)(z)]^\beta \prec z[\frac{z}{A_{\beta,\gamma}(g)(z)]^\beta $$ and we presented some particular cases of our main result.

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