Generalized hybrid (b, c)-inverses

Abstract

We study hybrid (b, c)-inverse in a more general setting. The new concept of right (m, n)-hybrid (b, c)-inverses is defined and studied. In particular, if m = n = 1, then right (m, n)-hybrid (b, c)-inverse is precisely the general right hybrid (b, c)-inverse. Some examples and counter-examples to illustrate the concepts and results are presented. Moreover, the relationship between right (m, n)-hybrid (b, c)-inverses, right hybrid (b, c)- inverses and (b, c)-inverses is studied. Various properties of right (m, n)-hybrid (b, c)-inverses are investigated. Some well-known results on right hybrid (b, c)-inverses are unified and extended.