ZEGHAD, Bochra2019-07-142019-07-142019http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/14943bstract In this work we will interest by the notion of relatively compact sets, we go on to study the space of ( p ,r )-compact operators and describe its structure as an operator ideal. We introduce the concept of Lipschitz ( p ,r )-compact operators. We show that can be seen as a natural extension of the linear case and we transfer some properties of the linear case into the Lipschitz setting.enCompact operators, ( p ,r )-compact operators, Ideal operators, Lipschitz p-compact operators, Relatively ( p ,r )-compact subsets.Thesis