An inequality for the entropy numbers and its application

We prove an inequality for the entropy numbers in terms of nonlinear Kolmogorov widths. This inequality is in the spirit of known inequalities of this type and it is adjusted to a form convenient in applications for m-term approximations with respect to a given system. Also, we obtain upper bounds for the m-term approximation by using the Weak Relaxed Greedy Algorithm with respect to a system which is not a dictionary.