New results on (b, c)–inverses

Abstract

In this paper, we present some necessary and sufficient conditions for the existence of the (b, c)-inverse and several representations for the (b, c)-inverse related to the group inverse. Since Mary inverse, core inverse, dual core inverse and Bott–Duffin (e, f)-inverse are all the special cases of the (b, c)-inverse, related results for these inverses are obtained.

Keywords:

• Generalized inverse
• (b
•  c)-inverse
• the inverse along an element
• core inverse
• dual core inverse
• Bott–Duffin (e
•  f)-inverse

AMS Subject Classifications:

• 15A09
• 16E50

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is grateful to China Scholarship Council for supporting her to purse her further study with Professor D. S. Cvetković-Ilić in University of Nis, Serbia. The research was supported by The National Natural Science Foundation of China [grant number 11371089], the Specialized Research Fund for the Doctoral Program of Higher Education [grant number 20120092110020], the Natural Science Foundation of Jiangsu Province [grant number BK20141327], the Foundation of Graduate Innovation Program of Jiangsu Province [grant number KYLX_0080], the Ministry of Education, Sciences and Technological Development, Republic of Serbia [grant number 174007], [grant number 174025].