• Bulletin of the Korean Mathematical Society
• /
• v.41 no.1
• /
• pp.109-116
• /
• 2004

In this paper, we study the uniqueness of entire functions and prove the following result: Let f(z) and g(z) be two nonconstant entire functions, $n\;{\geq}\;7$ a positive integer, and let a be a nonzero finite complex number. If $f^{n}(z)(f(z)\;-\;1)f'(z)\;and\;g^{n}(z)(g(z)\;-\;1)g'(z)$ share a CM, then $f(z)\;{\equiv}\;g(z)$. The result improves the theorem due to ref. [3].

• Journal of applied mathematics & informatics
• /
• v.35 no.5_6
• /
• pp.529-542
• /
• 2017

In this paper, using the notion of weakly weighted sharing and relaxed weighted sharing, we investigate the uniqueness problems of certain differential polynomials sharing a small function. The results obtained in this paper extend the theorem obtained by Jianren Long [9].

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.751-765
• /
• 2010

In this paper, we deal with a uniqueness theorem of two nonconstant meromorphic functions that share three values and one pair of polynomials. The results in this paper improve those given by G. G. Gundersen, G. Brosch and other authors.

• Honam Mathematical Journal
• /
• v.29 no.4
• /
• pp.695-700
• /
• 2007

We establish two uniqueness theorems for non-constant entire functions which extends results of J. S. Hwang in J. Math. Anal. and its Appl. Vol. 37 (1972) 452-456.

• Kyungpook Mathematical Journal
• /
• v.54 no.4
• /
• pp.511-519
• /
• 2014

In this paper, we prove two uniqueness theorem on meromorphic functions sharing one value which generalize a recent result of R. S. Dyavanal [2], and on the other hand, we relax the nature of sharing value from CM to IM.

• Kyungpook Mathematical Journal
• /
• v.56 no.3
• /
• pp.763-776
• /
• 2016

We prove a uniqueness theorem of entire functions sharing an entire function of smaller order with their linear differential polynomials. The results in this paper improve the corresponding results given by Gundersen-Yang[4], Chang-Zhu[3], and others. Some examples are provided to show that the results in this paper are best possible.

• Kyungpook Mathematical Journal
• /
• v.56 no.2
• /
• pp.419-430
• /
• 2016

In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.1089-1103
• /
• 2022

This paper focuses on the existence and uniqueness outcome for fractional integro-differential equation (FIDE) among impulsive edge condition and Hyers-Ulam-Rassias Stability (HURS) by using fractional calculus and some fixed point theorem in some weak conditions. The outcome procured in this paper upgrade and perpetuate some studied solutions.

• Communications of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.105-116
• /
• 2024

In this paper, we prove a uniqueness theorem of non-constant meromorphic functions of hyper-order less than 1 sharing two values CM and two partial shared values IM with their shifts. Our result in this paper improves and extends the corresponding results from Chen-Lin [2], Charak-Korhonen-Kumar [1], Heittokangas-Korhonen-Laine-Rieppo-Zhang [9] and Li-Yi [12]. Some examples are provided to show that some assumptions of the main result of the paper are necessary.

• East Asian mathematical journal
• /
• v.24 no.4
• /
• pp.399-405
• /
• 2008

In this paper, we get another proof of L. A. Rubel and C. C. Yang's theorem. It is more vivid technique. By using the relation between normal families and shared values we prove the theorem.