  This paper focuses on the study of MS-Lipschitz p-summing operators, which
were initially defined by the authors in <cite>14. Our objective is to
establish relationships between T and its linearizations, namely T and T.
Additionally, we extend our investigation by introducing a new definition in
the category of Lipschitz mappings defined on metric spaces, known as MS-Cohen
Lipschitz p-summing. We provide several results and characterizations for this
new concept.
