Regular Fredholm Relation Pairs

In this paper,the concept of Fredholm pairs for single valued operators is carried forward thecategory of multivalued linear operators .We get some elementary properties for Fredholmmultivalued linear operator pairs . Under some appropriate conditions,we get some resultsfor Fredholm multivalued linear operator pairs which are similar to that for the Fredholm op-erator pairs.What's more,in order to classify regular Fredholm relation pairs we still describesome sequences of subspaces.we introduce the notion of regular Fredholm relation pairs andsome preliminary and general results regarding regularity are also proved .Finnally,we tryour best to get four lemmas which can effectively transplant the classification of regularFredholm pairs to regular Fredholm relation pairs.