Abstract:
We study the symmetry for the generalized twisted Bernoulli polynomials and numbers. We give some interesting identities of the power sums and the generalized twisted Bernoulli polynomials using the symmetric properties for the -adic invariant integral.

Abstract:
We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function. We have the generating function of (h,q)-Genocchi polynomials. We define the Cangul-Ozden-Simsek's type twisted (h,q)-Genocchi polynomials and numbers. We also have the generalized twisted (h,q)-Genocchi numbers attached to the Dirichlet's character χ. Finally, we define zeta functions related to (h,q)-Genocchi polynomials and have the generating function of the generalized (h,q)-Genocchi numbers attached to χ.

Abstract:
We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function. We have the generating function of -Genocchi polynomials. We define the Cangul-Ozden-Simsek's type twisted -Genocchi polynomials and numbers. We also have the generalized twisted -Genocchi numbers attached to the Dirichlet's character . Finally, we define zeta functions related to -Genocchi polynomials and have the generating function of the generalized -Genocchi numbers attached to .

Abstract:
Recently, Choi et al. (2008) have studied the -extensions of theApostol-Bernoulli and the Apostol-Euler polynomials of order and multipleHurwitz zeta function. In this paper, we define Apostol's type -Euler numbers,, and -Euler polynomials ,,(). We obtain the generating functionsof ,,and ,,(), respectively. We also have the distribution relation forApostol's type -Euler polynomials. Finally, we obtain -zeta function associatedwith Apostol's type -Euler numbers and Hurwitz_s type -zeta functionassociated with Apostol's type -Euler polynomials for negative integers.

Abstract:
We investigate properties of identities and some interesting identities of symmetry for the Bernoulli polynomials of higher order using the multivariate -adic invariant integral on .

Abstract:
We investigate properties of identities and some interesting identities of symmetry for the Bernoulli polynomials of higher order using the multivariate p-adic invariant integral on p.

Abstract:
We derive formulae for the sums of products of the -Euler polynomials and numbers using the multivariate fermionic -adic -Volkenborn integral on .

Abstract:
The main purpose of this paper is to present new q-extensions of Apostol's type Euler polynomials using the fermionic p-adic integral on p. We define the q-λ-Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define q-extensions of Apostol type's Euler polynomials of higher order using the multivariate fermionic p-adic integral on p. We have the interpolation functions of these q-λ-Euler polynomials. We also give (h,q)-extensions of Apostol's type Euler polynomials of higher order and have the multiple Hurwitz type zeta functions of these (h,q)-λ-Euler polynomials.

Abstract:
The main purpose of this paper is to present new -extensions of Apostol's type Euler polynomials using the fermionic -adic integral on . We define the - -Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define -extensions of Apostol type's Euler polynomials of higher order using the multivariate fermionic -adic integral on . We have the interpolation functions of these - -Euler polynomials. We also give -extensions of Apostol's type Euler polynomials of higher order and have the multiple Hurwitz type zeta functions of these - -Euler polynomials.

Abstract:
We study the symmetric properties for the multivariate p-adic invariant integral on p related to the twisted generalized Euler polynomials of higher order.