Context :

Aims : We investigate observational constraints on the generalized Chaplygin gas ( GCG ) model including the gamma-ray bursts ( GRBs ) at high redshift obtained directly from the Union2 type Ia supernovae ( SNe Ia ) set .

Methods : By using the Markov Chain Monte Carlo method , we constrain the GCG model with the cosmology-independent GRBs , as well as the Union2 set , the cosmic microwave background ( CMB ) observation from the Wilkinson Microwave Anisotropy Probe ( WMAP7 ) result , and the baryonic acoustic oscillation ( BAO ) observation from the spectroscopic Sloan Digital Sky Survey ( SDSS ) data release 7 ( DR7 ) galaxy sample .

Results : The best-fit values of the GCG model parameters are A _ { S } = 0.7475 _ { -0.0539 } ^ { +0.0556 } ( 1 \sigma ) _ { -0.0816 } ^ { +0.0794 } ( 2 \sigma ) , \alpha = -0.0256 _ { -0.1326 } ^ { +0.1760 } ( 1 \sigma ) _ { -0.1907 } ^ { +0.2730 } ( 2 \sigma ) , and the effective matter density \Omega _ { m } = 0.2629 _ { -0.0153 } ^ { +0.0155 } ( 1 \sigma ) _ { -0.0223 } ^ { +0.0236 } ( 2 \sigma ) , which are more stringent than previous results for constraining GCG model parameters .

Conclusions :