A three-parameter difference Hamiltonian operator, corresponding pair of Hamiltonian operators and a family of Liouville integrable lattice equations

A difference Hamiltonian operator involved three arbitrary real parameters is introduced. When these parameters in the difference Hamiltonian operator are properly chosen, we obtain a pair of difference Hamiltonian operators. Then, using Magri scheme of bi-Hamiltonian formulation, we construct a family of Liouville integrable lattice equations. Finally, the discrete zero curvature representation of obtained family is presented.