Résumé:
The context of this thesis falls within the framework of functional analysis
and more precisely in nonlinear geometry. The ideas of this work were inspired from the
article of J.D. Farmer and W.B. Jonhnson entitled "Lipschitz p-summing operators" and
from the paper of R. Khalil and W. Deeb entitled " -summing operators in Banach spaces";
also that of K. Saadi entitled "On the composition ideals of Lipschitz mappings".
In the rst part, our contribution consisted in the following idea: from a linear -summing
operator between Banach spaces, where is a modulus function, we have introduced the
notion of Lipschitz -summing operator between metric spaces giving a nonlinear version of
Pietsch domination theorem for these operators and some properties concerning this class.
In the second part, from the notion of Lipschitz strictly p-summing operators we have
given new characterizations of this class, where we have adapted this de nition for constructing
other class of Lipschitz mappings which are called M-strictly lipschiz p-summing
operators and strictly Lipschitz p-nuclear operators and strictly Lipschitz (p; r; s)-summing
operators, in addition to all that, we obtained also some interesting results for these new
classes.
In the end of this thesis, we present a short section collecting some interesting open
problems.