  The mechanical properties of biological membranes play an important role in
the structure and the functioning of living organisms. One of the most widely
used methods for determination of the bending elasticity modulus of the model
lipid membranes (simplified models of the biomembranes with similar mechanical
properties) is analysis of the shape fluctuations of the nearly spherical lipid
vesicles. A theoretical basis of such an analysis is developed by Milner and
Safran. In the present studies we analyze their results using an approach based
on the Bogoljubov inequalities and the approximating Hamiltonian method. This
approach is in accordance with the principles of statistical mechanics and is
free of contradictions. Our considerations validate the results of Milner and
Safran if the stretching elasticity K_s of the membrane tends to zero.
