• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.221-236
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• 2002

Using the p-adic q-integral due to T. Kim[4], we define a number B＊$_{n}$(q) and a polynomial B＊$_{n}$(q) which are p-adic q-analogue of the ordinary Bernoulli number and Bernoulli polynomial, respectively. We investigate some properties of these. Also, we give slightly different construction of Tsumura＇s p-adic function $\ell$$_{p}$(u, s, $\chi$) [14] using the p-adic q-integral in [4].n [4].

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.493-511
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• 2009

Let $q\;{\geq}\;3$ be an odd integer and a be an integer coprime to q. Denote by N(a, q) the number of pairs of integers b, c with $bc\;{\equiv}\;a$ (mod q), $1\;{\leq}\;b$, $c\;{\leq}\;{\frac{q-1}{2}}$ and with b, c having different parity. The main purpose of this paper is to study the sum ${\sum}^{'q}_{a=1}\;\(N(a,\;q)\;-\;\frac{{\phi}(q)}{8}\)^2$ and obtain a sharp asymptotic formula.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.321-325
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• 2012

In this paper, we consider twisted $q$-Euler polynomials and define a $p$-adic $q$-transfer operator (see [6]). From this operator, we investigate the eigenvalues of the $p$-adic $q$-transfer operator on the space of twisted $q$-Euler polynomials.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.555-565
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• 2018

The main subject of this paper is to introduce the (p, q)-Euler polynomials and obtain several interesting symmetric properties of the modified (p, q)-Hurwitz Euler Zeta function with regard to (p, q) Euler polynomials. In order to get symmetric properties, we introduce the new (p, q)-analogue of Euler polynomials $E_{n,p,q}(x)$ and numbers $E_{n,p,q}$.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.243-268
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• 2019

The main aim of this paper is to study some growth properties of composite entire functions on the basis of relative $(p,q)-{\varphi}$ type and relative $(p,q)-{\varphi}$ weak type where p and q are any two positive integers and ${\varphi}(r):[0,+{\infty}){\rightarrow}(0,+{\infty})$ be a non-decreasing unbounded function.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.819-845
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• 2020

In this paper, we established sum and product theorems connected to (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weak type of entire functions of several complex variables with respect to another one under somewhat different conditions.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.57-72
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• 2021

In this paper, we construct q-cosine and sine Genocchi polynomials using q-analogues of addition, subtraction, and q-trigonometric function. From these polynomials, we obtain some properties and identities. We investigate some symmetric properties of q-cosine and sine Genocchi polynomials. Moreover, we find relations between these polynomials and others polynomials.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.69-91
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• 2022

In the paper we establish some new results depending on the comparative growth properties of composite transcendental entire and meromorphic functions using relative (p, q, t)L-th order, relative (p, q, t)L-th type and relative (p, q, t)L-th weak type and that of Wronskian generated by one of the factors.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.207-213
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• 2010

In this paper, we define the q-extension of the Hardy-Littlewood-type maximal operator related to q-Volkenborn integral. By the meaning of the extension of q-Volkenborn integral, we obtain the boundedness of the q-extension of the Hardy-Littlewood-type maximal operator in the p-adic integer ring.

• 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.