The main purpose of this paper is to study generating functions of the q -Genocchi numbers and polynomials. We prove a new relation for the generalized q -Genocchi numbers, which is related to the q -Genocchi numbers and q -Bernoulli numbers. By applying Mellin transformation and derivative operator to the generating functions, we define q -Genocchi zeta and l -functions, which are interpolated q -Genocchi numbers and polynomials at negative integers. We also give some applications of the generalized q -Genocchi numbers.