  A general deterministic analysis to state the necessary conditions with a
coefficient determination for the variational source condition to hold is
provided. Of particular interest in terms of the choice of the regularization
parameter, it is revealed that Morozov's discrepancy principle can be used both
for determining new stable lower and upper bounds for the regularization
parameter. With these bounds, it is also possible to establish quantitative
estimations for the index function as well as for the different definitions of
the Bregman distance. Inclusion of the variational source condition into the
stability analysis enables one to re-establish convergence and convergence rate
results in terms of the index function. The coefficient in the variational
source condition is explicitly defined as a multivariable function of constants
in Morozov's discrepancy principle. As expected, the results here are
applicable when any strictly convex, smooth/non-smooth objective functional is
considered.
