  Multi-wavelength analyses of spectra of active galactic nuclei (AGNs) provide
useful information on the physical processes in the accretion disk and jets of
black holes. This, however, is limited to bright sources and may not represent
the population as a whole. Another approach is through the investigation of the
cosmological evolution of the luminosity function (LF) that shows varied
evolution (luminosity and density) at different wavelengths. These differences
and the correlations between luminosities can shed light on the Jet-accretion
disk connection. Most such studies use forward fitting parametric methods that
involve several functions and many parameters. We use non-parametric,
non-binning methods developed by Efron and Petrosian, and Lynden-Bell, for
obtaining unbiased description of the evolution of the LF, from data truncated
by observational selection effects. We present analysis of the evolution of
gamma-ray LF of blazars with main focus on flat spectrum radio quasars (FSRQs).
This requires analysis of both gamma-ray and optical data, essential for
redshift measurements, and a description of the joint LF. We use a new approach
which divides the sample into two sub-samples, each with its own flux limit. We
use the Fermi-LAT and GAIA observations, and present results on the gamma-ray
LF and its evolution, and determine the intrinsic correlation between the
gamma-ray and optical luminosities corrected for the well known false
correlation induced by their similar redshift dependence and evolution of the
two luminosities. We also present a direct estimation of the contribution of
blazars to the spectrum of the extragalactic gamma-ray background.
