• East Asian mathematical journal
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• 제36권1호
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• pp.13-24
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• 2020

The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations. We also obtain integral representations, implicit and explicit formulas and relations for these polynomials and numbers. Furthermore, we consider some relationships for Apostol type (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.

• Journal of applied mathematics & informatics
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• 제37권3_4호
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• pp.295-305
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• 2019

In the present paper, we introduce (p, q)-Frobenius-Genocchi numbers and polynomials and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, implicit and explicit formulas and relations for these polynomials and numbers. We consider some relationships for (p, q)-Frobenius-Genocchi polynomials of order ${\alpha}$ associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.373-386
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• 2023

In this paper we have obtained various forms of (p, q)-analogue of Aleph-Function satisfying Truesdell's ascending and descending F_p,q-equation. These structures have been employed to arrive at certain generating functions for (p, q)-analogue of Aleph-Function. Some specific instances of these outcomes as far as (p, q)-analogue of I-function, H-function and G-functions have likewise been obtained.

• Korean Journal of Mathematics
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• 제31권2호
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• pp.229-242
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• 2023

In this paper, we investigate the [p, q] - φ order and [p, q] - φ type of f₁ + f₁, ${\frac{f_1}{f_2}}$ and f₁ f₁, where f₁ and f₁ are analytic or meromorphic functions with the same [p, q]-φ order and different [p, q]-φ type in the unit disc. Also, we study the [p, q]-φ order and [p, q]-φ type of different f and its derivative. At the end, we investigate the relationship between two different [p, q] - φ convergence exponents of f. We extend some earlier precedent well known results.

• Journal of applied mathematics & informatics
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• 제41권4호
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• pp.753-763
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• 2023

In this paper, we introduce a fully modified (p, q)-poly tangent polynomials and numbers of the first type. We investigate analytic properties that is related with (p, q)-Gaussian binomial coefficients. We also define (p, q)-Stirling numbers of the second kind and fully modified (p, q)-poly tangent polynomials and numbers of the first type with two variables. Moreover, we derive some identities are concerned with the modified tangent polynomials and the (p, q)-Stirling numbers.

• 대한수학회지
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• 제44권1호
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• pp.1-10
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• 2007

The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p-adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted q-Bernoulli numbers. This is the generalization of Kim's h-extension of p-adic q-L-function which was constructed in [5] and is a partial answer for the open question which was remained in [3].

• 한국학교수학회논문집
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• 제17권4호
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• pp.805-816
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• 2014

본 연구에서는 형식적 함의에 대한 역사적 발달과정을 살펴보고 형식적 함의에 대하여 대학생들이 어떻게 이해하는지를 분석하였다. 또한 고등학생들과 예비대학생들을 대상으로 카드모임에 대한 실제적 함의에 대하여 조사한 결과 주어진 카드 모음에서 성립하는 패턴을 명제 $p{\rightarrow}q$로 나타낼 때에는 명제 $p{\rightarrow}q$를 ${\sim}p{\vee}q$와 동치인 명제로 이해하는 학생들이 가장 많았지만 명제 $p{\rightarrow}q$가 성립하는 카드를 모으는 과정에서는 조건명제 $p{\rightarrow}q$를 $p{\wedge}q$와 동치인 명제로 이해하는 학생들이 가장 많은 것으로 조사되었다.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.303-311
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• 2017

In this paper we define (p, q)-analogue of Euler zeta function. In order to define (p, q)-analogue of Euler zeta function, we introduce the (p, q)-analogue of Euler numbers and polynomials by generalizing the Euler numbers and polynomials, Carlitz's type q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Euler numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Euler polynomials by using computer.

• 대한수학회지
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• 제39권2호
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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].

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.75-98
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• 2021

In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p, q)-Fekete-Szegö inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.