In the paper, we introduce an analogue of Haar distribution based on (rho, q)-numbers, as follows: mu(rho,q) (a + p(N)Z(p)) = rho(pN)/[p(N)](rho,q) (q/rho)(a) By means of this distribution, we derive (rho, q)-analogue ...

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 ...

In this paper, we first consider a generalization of Kim's p-adic q-integral on Z p including parameters α and β. By using this integral, we introduce the q-Daehee polynomials and numbers with weight α,β. Then, we obtain ...

In this paper, we introduce the generating function of Hermite-based poly-Daehee numbers and polynomials. By making use of this generating function, we investigate some new and interesting identities for the Hermite-based ...

We consider a new class of generating functions of the generalizations of Bernoulli and Euler polynomials in terms of (p, q)-integers. By making use of these generating functions, we derive (p, q)-generalizations of several ...

In this work, we introduce a class of a new generating function for (p, q)-analog of Apostol type polynomials of order a including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order alpha. By making ...

Motivated by the paper of Kim et al. [T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, D. V. Dolgy, J. Nonlinear Sci. Appl., 9 (2016), 1077-1082], we study a class of q-Euler polynomials earlier given by Kim et al. in [T. Kim, ...

In the paper, we derive some new symmetric identities of q-Genocchi polynomials arising from the fermionic p-adic q-integral on Z(p).

In this paper, we develop the theory of the multiple q-analogue of the Heine's binomial formula, chain rule and Leibniz's rule. We also derive many useful definitions and results involving multiple q-antiderivative and ...

Recently, Sofonea (Gen. Math. 16:47-54, 2008) considered some relations in the context of quantum calculus associated with the q-derivative operator D-q and divided difference. As applications of the post-quantum calculus ...