• 대한수학회논문집
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• 제31권2호
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• pp.295-309
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• 2016

The paper deals with the problem of meromorphic functions sharing a small function with its differential polynomials and improves the results of Liu and Gu [9], Lahiri and Sarkar [8], Zhang [13] and Zhang and Yang [14] and also answer some open questions posed by Kit-Wing Yu [16]. In this paper we provide some examples to show that the conditions in our results are the best possible.

• 대한수학회지
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• 제50권4호
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• pp.847-864
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• 2013

By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the $y$-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.217-232
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• 2011

Differential subordination and superordination results are obtained for multivalent meromorphic functions associated with the Liu-Srivastava linear operator in the punctured unit disk. These results are derived by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained.

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.195-204
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• 2011

We prove a uniqueness theorem for meromorphic functions sharing three weighted values, which improves a result given by N. Terglane in 1989 and a result given by X. M. Li and H. X. Yi in 2003. Some examples are provided to show that the result of the paper is best possible.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.631-646
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• 2009

In the present investigation, we introduce new classes of p-valent meromorphic functions defined by Liu-Srivastava linear operator and the multiplier transform and study their properties by using certain first order differential subordination and superordination.

• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.43-58
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• 2011

Using the notion of weighted sharing of values we study the uniqueness of meromorphic functions when certain non-linear differential polynomials share the same 1-points. Though the main concern of the paper is to improve a result of Fang [5] but as a consequence of the main result we improve and supplement some former results of Lahiri-Sarkar [16], Fang-Fang[6] et. al.

• 충청수학회지
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• 제31권1호
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• pp.103-130
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• 2018

In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative $_pL^*-order$, relative $_pL^*-lower$ order and differential monomials, differential polynomials generated by one of the factors.

• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.169-180
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• 2006

This paper proves the following results: Let $f$ be a transcendental entire function, and let $k({\geq})2$ be a positive integer. If $T(r,\;f){\neq}N_{1)}(r,1/f)+S(r,\;f)$, then $ff^{(k)}$ assumes every finite nonzero value infinitely often. Also the case when f is a transcendental meromorphic function has been considered and some results are obtained.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권2호
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• pp.141-148
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• 1995

In this paper we shall consider function p(z) analytic in the open unit circle D and the solutions y(z) of the differential equation y"(Z) ＋ p(z)y(z) = 0. (1.1) The ratio f(z) = u(z)/v(z) of any two independent solutions u(z) and v(z) of (1.1) will be function f(z), meromorphic in D with only simple poles, and such that f'(z) (equation omitted) 0. We shall say that a meromorphic function which satisfies these two condition belongs to the restricted class.(omitted)

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.451-464
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• 2016

In this paper, we investigate the uniqueness problem of a meromorphic function sharing one small function with its differential polynomial, and give a result which is related to a conjecture of R. $Br{\ddot{u}}ck$.