Abstract
Consider a prime ring which is noncommutative with the maximal left ring of quotients of denoted by and the extended centroid . An additive map satisfying for all , where is called a weak Jordan right η-centralizer. In this paper, we establish the characterization of weak Jordan right η-centralizers in prime rings. As an application, we describe X-generalized skew derivations which behave like weak Jordan right η-centralizers.