• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.271-283
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• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.167-179
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• 2023

In this paper, we investigate solutions of equations which are linear (p, q)-difference equation of higher order by using (p, q)-derivative and integral. We also derive the solution of equation in the case of second order.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.439-448
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• 2023

We introduce several higher-order (p, q)-differential equation of which are related to (p, q)-Bernoulli polynomials. We also find some relations between (p, q)-Bernoulli, (p, q)-Euler, and (p, q)-Genocchi polynomials.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.2
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• pp.11-20
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• 2002

In this paper, for many prime power q, it is shown that new cyclic relative difference sets with parameters (equation omitted) can be constructed by using d-homogeneous functions on $F_{q^{n}}${0} over $F_{q}$ with difference-balanced property, where $F_{q^{n} }$ is a finite field with $q^{n}$ elements. Several new cyclic relative difference sets with parameters (equation omitted) are constructed by using p-ary sequences of period $q^{n}$ -1 with ideal autocorrelation property introduced by Helleseth and Gong and d-form sequences.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.447-456
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• 2015

In this paper, we investigate the differential-difference equation $(f(z+c)-f(z))^2+P(z)^2(f^{(k)}(z))^2=Q(z)$, where P(z), Q(z) are nonzero polynomials. In addition, we also investigate Fermat type q-difference differential equations $f(qz)^2+(f^{(k)}(z))^2=1$ and $(f(qz)-f(z))^2+(f^{(k)}(z))^2=1$. If the above equations admit a transcendental entire solution of finite order, then we can obtain the precise expression of the solution.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.1
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• pp.21-32
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• 2002

In this paper, for any prime q, new cyclic difference sets with Singer parameter equation omitted are constructed by using the q-ary sequences (d-homogeneous functions) of period $q_n$-1. When q is a power of 3, new cyclic difference sets with Singer parameter equation omitted are constructed from the ternary sequences of period $q_n$-1 with ideal autocorrealtion found by Helleseth, Kumar and Martinsen.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.983-1002
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• 2021

We investigate the non-existence of finite order transcendental entire solutions of Fermat-type differential-difference equations [f(z)f'(z)]ⁿ + P²(z)f^m(z + 𝜂) = Q(z) and [f(z)f'(z)]ⁿ + P(z)[∆_𝜂f(z)]^m = Q(z), where P(z) and Q(z) are non-zero polynomials, m and n are positive integers, and 𝜂 ∈ ℂ \ {0}. In addition, we discuss transcendental entire solutions of finite order of the following Fermat-type differential-difference equation P²(z) [f^(k)(z)]² + [αf(z + 𝜂) - 𝛽f(z)]² = e^r(z), where $P(z){\not\equiv}0$ is a polynomial, r(z) is a non-constant polynomial, α ≠ 0 and 𝛽 are constants, k is a positive integer, and 𝜂 ∈ ℂ \ {0}. Our results generalize some previous results.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.425-438
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• 2007

In this paper, we establish some new oscillation criteria for a second-order delay dynamic equation $$u^{{\Delta}{\Delta}}(t)+p(t)u(\tau(t))=0$$ on a time scale $\mathbb{T}$. The results can be applied on differential equations when $\mathbb{T}=\mathbb{R}$, delay difference equations when $\mathbb{T}=\mathbb{N}$ and for delay $q$-difference equations when $\mathbb{T}=q^{\mathbb{N}}$ for q > 1.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.153-164
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• 2010

We study the global asymptotic stability, the character of the semicycles, the periodic nature and oscillation of the positive solutions of the difference equation $x_{n+1}=\frac{p+x_{n-k}}{q+x_n}+\frac{x_{n-k}}{x_n}$, n=0, 1, 2, ${\cdots}$. where p, q ${\in}$ (0, ${\infty}$), q ${\neq}$ 2, k ${\in}$ {1, 2, ${\cdots}$} and the initial values $x_{-k}$, ${\cdots}$, $x_0$ are arbitrary positive real numbers.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.125-131
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• 1999

We obtain some sufficient conditions for oscillation of the neutral difference equation with positive and negative coefficients $${\Delta}(x_n-cx_{n-m})+px_{n-k}-qx_{n-l}=0$$, where ${\Delta}$ denotes the forward difference operator, m, k, l, are nonnegative integers, and $c{\in}[0,1),p,q{\in}\mathbb{R}^+$.