• Bulletin of the Korean Mathematical Society
• /
• v.59 no.5
• /
• pp.1105-1117
• /
• 2022

In this paper, we obtain a second main theorem for holomorphic curves and moving hyperplanes of Pⁿ(C) where the counting functions are truncated multiplicity and have different weights. As its application, we prove a uniqueness theorem for holomorphic curves of finite growth index sharing moving hyperplanes with different multiple values.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.345-350
• /
• 2015

In the paper we prove a uniqueness theorem which improves and generalizes a number of uniqueness theorems for meromorphic functions related to Nevanlinna's five value theorem.

• Journal of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.467-482
• /
• 2010

We prove a uniqueness theorem for meromorphic functions sharing three weighted values which improves some existing results.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.171-177
• /
• 2018

In this research paper considering a differential equation with impulsive effect and dependent delay and applied Banach fixed point theorem using the impulsive condition to the impulsive fractional functional differential equation of an order ${\alpha}{\in}(1,2)$ to get an uniqueness solution. At last, theorem is verified by using a numerical example to illustrate the uniqueness solution.

• Kyungpook Mathematical Journal
• /
• v.58 no.2
• /
• pp.291-305
• /
• 2018

In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.

• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.985-999
• /
• 2018

This paper is devoted to the existence and uniqueness of $L^p$ (p > 1) solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator g satisfies a ($p{\wedge}2$)-order weak monotonicity condition in y and a Lipschitz continuity condition in z, both non-uniformly in t. The corresponding stability theorem and comparison theorem are also proved.

• Honam Mathematical Journal
• /
• v.29 no.2
• /
• pp.119-192
• /
• 2007

A very important Hopf algebra is the graded Hopf algebra Symm of symmetric functions. It can be characterized as the unique graded positive selfdual Hopf algebra with orthonormal graded distinguished basis and just one primitive element from the distinguished basis. This result is due to Andrei Zelevinsky. A noncommutative graded Hopf algebra of this type cannot exist. But there is a most important positive graded Hopf algebra with distinguished basis that is noncommutative and that is twisted selfdual, the Malvenuto-Poirier-Reutenauer Hopf algebra of permutations. Thus the question arises whether there is a corresponding uniqueness theorem for MPR. This prepreprint records initial investigations in this direction and proves that uniquenees holds up to and including the degree 4 which has rank 24.

• Journal of applied mathematics & informatics
• /
• v.38 no.5_6
• /
• pp.415-426
• /
• 2020

In this paper, we will prove some uniqueness theorems that can be applied to the generalized Hyers-Ulam stability of some additive-quadratic-cubic functional equation in complete modular spaces without Δ₂-conditions.

• Journal of applied mathematics & informatics
• /
• v.31 no.5_6
• /
• pp.877-894
• /
• 2013

In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.631-640
• /
• 2007

The purpose of this article is to deal with the multiple values and uniqueness of meromorphic functions with small functions in the whole complex plane. We obtain a more general theorem which improves and extends strongly the results of R. Nevanlinna, Li-Qiao, Yao, Yi, and Thai-Tan.