Interpolation of q-analogue of multiple zeta and zeta-star values

In this paper, we consider such two generalizations simultaneously, that is, we compose polynomials, called t-qMZVs, interpolating qMZVs and qMZSVs using a parameter t which are reduced to qMZVs as t=0, to qMZSVs as t=1, and to t-MZVs as q→1. Then we prove Kawashima type relation, cyclic sum formula and Hoffman type relation for t-qMZVs.