• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.133-147
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• 2021

Our aim in this paper is to derive several new monotonicity properties and functional inequalities of some functions involving the q-gamma, q-digamma and q-polygamma functions. More precisely, some classes of functions involving the q-gamma function are proved to be logarithmically completely monotonic and a class of functions involving the q-digamma function is showed to be completely monotonic. As applications of these, we offer upper and lower bounds for this special functions and new sharp upper and lower bounds for the q-analogue harmonic number harmonic are derived. Moreover, a number of two-sided exponential bounding inequalities are given for the q-digamma function and two-sided exponential bounding inequalities are then obtained for the q-tetragamma function.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.755-772
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• 2023

Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) and Fox-Wright function _rΨ_s(z).

• Journal of applied mathematics & informatics
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• v.41 no.2
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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.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.37-56
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• 2020

In this paper we discuss some interesting properties of (p, q)-special polynomials and derive various relations. We gain some relations between (p, q)-zeta function and (p, q)-special polynomials by considering (p, q)-analogue Euler sum types. In addition, we derive the relationship between (p, q)-polylogarithm function and (p, q)-special polynomials.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1155-1161
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• 2014

In this paper, we rederive the identity ${\Gamma}_q(x){\Gamma}_q(1-x)={\frac{{\pi}_q}{sin_q({\pi}_qx)}$. Then, we give q-analogue of Gauss' multiplication formula and study representation of q-oscillator algebra in terms of the q-factorial polynomials.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.9-15
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• 2016

In this paper, the authors establish some double inequalities concerning the (q, k)-deformed Gamma function. These inequalities emanate from certain problems of traffic flow. The procedure makes use of the integral representation of the (q, k)-deformed Gamma function.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.541-552
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• 2021

In this paper, we introduce q-sigmoid polynomials combining q-cosine function. We find several properties and identities of these polynomials which are related to sigmoid function using deep learning.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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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.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.463-487
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• 2019

In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q, t)L-th order and relative (p, q, t)L-th type of entire and meromorphic function with respect to another entire function.

• The Pure and Applied Mathematics
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• v.26 no.1
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• pp.13-33
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• 2019

The main aim of this paper is to establish some comparative growth properties of composite entire functions on the basis of their relative (p, q)-th order, relative (p, q)-th lower order, relative (p, q)-th type, relative (p, q)-th weak type of entire function with respect to another entire function where p and q are any two positive integers.