Recently, many mathematicians have studied various kinds of the q-analogue of Genocchi numbers and polynomials. In the work New approach to q-Euler, Genocchi numbers and their interpolation functions, "Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105-112, 2009.", Kim defined new generating functions of q-Genocchi, q-Euler polynomials, and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type qzeta function. This function interpolates q-Genocchi polynomials at negative integers. Finally, we also give some identities related to these polynomials.

In 2009, Kim et al. gave some identities of symmetry for the twisted Euler polynomials of higherorder, recently. In this paper, we extend our result to the higher-order twisted q-Euler numbers and polynomials. The purpose of this paper is to establish various identities concerning higherorder twisted q-Euler numbers and polynomials by the properties of p-adic invariant integral on Z p . Especially, if q 1, we derive the result of .

This paper performs a further investigation on the q-Bernoulli polynomials and numbers given by Açikgöz et al. (Adv. Differ. Equ. 2010, 9, Article ID 951764) some incorrect properties are revised. It is pointed out that the definition concerning the q-Bernoulli polynomials and numbers is unreasonable. The purpose of this paper is to redefine the q-Bernoulli polynomials and numbers and correct its wrong properties and rebuild its theorems.

A systemic study of some families of -Genocchi numbers and families of polynomials of Nörlund type is presented by using the multivariate fermionic -adic integral on . The study of these higher-order -Genocchi numbers and polynomials yields an interesting -analog of identities for Stirling numbers.

Recently, many authors have studied twisted q-Bernoulli polynomials by using the p-adic invariant q-integral on Z p. In this paper, we define the twisted p-adic q-integral on Z p and extend our result to the twisted q-Bernoulli polynomials and numbers. Finally, we derive some various identities related to the twisted q-Bernoulli polynomials.