Cosmography approach to dark energy cosmologies: new constrains using
  the Hubble diagrams of supernovae, quasars and gamma-ray bursts
  In the context of cosmography approach and using the data of Hubble diagram
for supernovae, quasars and gamma-ray bursts, we study some DE parametrizations
and also the concordance $\Lambda$CDM universe. Using the different
combinations of data sample including ({\it i}) supernovae (Pantheon), ({\it
ii}) Pantheon + quasars and ({\it iii}) Pantheon + quasars + gamma-ray bursts
and applying the minimization of $\chi^2$ function of distance modulus of data
samples in the context of Markov Chain Monte Carlo method, we first obtain the
constrained values of the cosmographic parameters in model independent
cosmography scenario. We then investigate our analysis, for different
concordance $\Lambda$CDM cosmology, $w$CDM, CPL and Pade parametrizations.
Comparing the numerical values of the cosmographic parameters obtained for DE
scenarios with those of the model independent method, we show that the
concordance $\Lambda$CDM model has a serious tension when we involve the
quasars and gamma-ray bursts data in our analysis. While the high redshift
quasars and gamma-ray bursts can falsify the concordance model, our results of
cosmography approach indicate that the other DE parametrizations are still
consistent with these observations.
