We here propose a new model-independent technique to overcome the circularity problem affecting the use of gamma-ray bursts (GRBs) as distance indicators through the use of E_p_-E_iso_ correlation. We calibrate the E_p_-E_iso_ correlation and find the GRB distance moduli that can be used to constrain dark energy models. We use observational Hubble data to approximate the cosmic evolution through Bezier parametric curve obtained through the linear combination of Bernstein basis polynomials. In doing so, we build up a new data set consisting of 193 GRB distance moduli. We combine this sample with the supernova JLA data set to test the standard {Lambda}CDM model and its wCDM extension. We place observational constraints on the cosmological parameters through Markov Chain Monte Carlo numerical technique. Moreover, we compare the theoretical scenarios by performing the Akaike and Deviance Information statistical criteria.the 2{sigma} level, while for the wCDM model we obtain {Omega}m=0.34^+0.13^-0.15 and w=-0.86^+0.36^-0.38 at the 2{sigma} level. Our analysis suggests that {Lambda}CDM model is statistically favoured over the wCDM scenario. No evidence for extension of the {Lambda}CDM model is found.

Cone search capability for table J/MNRAS/486/L46/tablea1 (List of the full GRBs used in this work and their redshift z and calibrated muGRB)