We consider weighted -Genocchi numbers and polynomials. We investigated some interesting properties of the weighted -Genocchi numbers related to weighted -Bernstein polynomials by using fermionic -adic integrals on .

In the present paper, we introduce a new kind of Bernoulli, Euler and Genocchi polynomials based on the (p; q)-calculus and investigate their some properties involving addition theorems, di¤erence equations, derivative properties, recurrence relationships, and so on. We also derive (p; q)-analogues of some known formulae belong to usual Bernoulli, Euler and Genocchi polynomials. Moreover, we get (p; q)-extension of Cheon's main result in [6]. Furthermore, we discover (p; q)-analogue of the main results given earlier by Srivastava and Pintér in [26].

No abstract

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 known as the (p, q)-calculus, we derive several relations involving the (p, q)-derivative operator and divided differences.MSC: Primary 11B68; 11B83; secondary 81S40

No abstract