Testing the Distance-Duality Relation from Strong Gravitational Lensing,
  Type Ia Supernovae and Gamma-Ray Bursts Data up to redshift $z\sim3.6$
  In this paper, we perform a cosmological model-independent test of the cosmic
distance-duality relation (CDDR) in terms of the ratio of angular diameter
distance (ADD) $D=D_{\rm A}^{\rm sl}/D_{\rm A}^{\,\rm s}$ from strong
gravitational lensing (SGL) and the ratio of luminosity distance (LD)
$D^\ast=D_{\rm L}^{\,\rm l}/D_{\rm L}^{\,\rm s}$ obtained from the joint of
type Ia supernovae (SNIa) Union2.1 compilation and the latest Gamma-Ray Bursts
(GRBs) data, where the superscripts s and l correspond to the redshifts
$z_{\,\rm s}$ and $z_{\,\rm l}$ at the source and lens from SGL samples. The
purpose of combining GRB data with SNIa compilation is to test CDDR in a wider
redshift range. The LD associated with the redshits of the observed ADD, is
obtained through two cosmological model-independent methods, namely, method A:
binning the SNIa+GRBs data, and method B: reconstructing the function of DL by
combining the Crossing Statistic with the smoothing method. We find that CDDR
is compatible with the observations at $1\sigma$ confidence level for the power
law model which is assumed to describe the mass distribution of lensing systems
with method B in a wider redshift range.
