Cheng, Chuangxun Lo, Wen-Lung Xu, Hailong
Published in
Banach Journal of Mathematical Analysis

In this paper, we study continuous frames from projective representations of locally compact abelian groups of type G^×G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$...

Kim, Taekyun Kim, Dae San Kim, Han Young Kwon, Jongkyum
Published in
Journal of Inequalities and Applications

Identities of symmetry in two variables for Bernoulli polynomials and power sums had been investigated by considering suitable symmetric identities. T. Kim used a completely different tool, namely the p-adic Volkenborn integrals, to find the same identities of symmetry in two variables. Not much later, it was observed that this p-adic approach can ...

Sharma, Sunil Kumar Khan, Waseem A. Araci, Serkan Ahmed, Sameh S.
Published in
Advances in Difference Equations

Kim et al. (Proc. Jangjeon Math. Soc. 21(4):589–598, 2018) have studied the central Fubini polynomials associated with central factorial numbers of the second kind. Motivated by their work, we introduce degenerate version of the central Fubini polynomials. We show that these polynomials can be represented by the fermionic p-adic integral on Zp\docu...

Ma, Yuankui Kim, Taekyun
Published in
Advances in Difference Equations

In this paper, we introduce one discrete random variable, namely the negative λ-binomial random variable. We deduce the expectation of the negative λ-binomial random variable. We also get the variance and explicit expression for the moments of the negative λ-binomial random variable.

Duran, Ugur Acikgoz, Mehmet Araci, Serkan
Published in
Advances in Difference Equations

Kim and Kim (Russ. J. Math. Phys. 26(1):40–49, 2019) have studied the type 2 poly-Bernoulli polynomials. Inspired by their work, we consider a new class of the Frobenius–Genocchi polynomials, which is called the type 2 poly-Frobenius–Genocchi polynomials, by means of the polyexponential function. We also derive some new relations and properties inc...

Gun, Damla Simsek, Yilmaz
Published in
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

The aim of this paper is to give some new relations, identities, and inequalities for the Bernoulli polynomials and numbers of higher order, the Stirling numbers of the second kind, the Eulerian numbers, and the Catalan numbers. By applying the Laplace transformation to the generating function of the Bernoulli polynomials of higher order, a novel f...

Jang, Lee-Chae Kim, Dae San Kim, Taekyun Lee, Hyunseok
Published in
Advances in Difference Equations

In this paper, by means of p-adic Volkenborn integrals we introduce and study two different degenerate versions of Bernoulli polynomials of the second kind, namely partially and fully degenerate Bernoulli polynomials of the second kind, and also their higher-order versions. We derive several explicit expressions of those polynomials and various ide...

Kim, Taekyun Kim, Dae San Kim, Han Young Kwon, Jongkyum
Published in
Journal of Inequalities and Applications

In this paper, we study some identities on Euler numbers and polynomials, and those on degenerate Euler numbers and polynomials which are derived from the fermionic p-adic integrals on Zp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepa...

Kim, Dae San Kim, Taekyun Kim, Han Young Kwon, Jongkyum
Published in
Journal of Inequalities and Applications

As is well known, power sums of consecutive nonnegative integers can be expressed in terms of Bernoulli polynomials. Also, it is well known that alternating power sums of consecutive nonnegative integers can be represented by Euler polynomials. In this paper, we show that power sums of consecutive positive odd q-integers can be expressed by means o...

Kim, Won Joo Kim, Dae San Kim, Han Young Kim, Taekyun
Published in
Journal of Inequalities and Applications

In this paper, we investigate some properties and identities for degenerate Euler polynomials in connection with degenerate Bernstein polynomials by means of fermionic p-adic integrals on Zp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \us...