A generalization of the MP-m-WGI

References

• O.M. Baksalary and G. Trenkler, Core inverse of matrices, Linear Multilinear Algebra 58(6) (2010), 681–697. doi: 10.1080/03081080902778222
   Web of Science ®Google Scholar
• A. Ben-Israel and T.N.E. Greville, Generalized inverses, Theory and applications, Second edition, Canadian Mathematical Society, Springer, New York/Berlin/Heidelberg/Hong Kong/London/Milan/Paris/Tokyo, 2003.
   Google Scholar
• D.E. Ferreyra, F.E. Levis, and N. Thome, Maximal classes of matrices determining generalized inverses, Appl. Math. Comput. 333 (2018), 42–52.
   Web of Science ®Google Scholar
• D.E. Ferreyra and S.B. Malik, A generalization of the group inverse, Quaest. Math. 46(10) (2023), 2129–2145. doi: 10.2989/16073606.2022.2144533
   Web of Science ®Google Scholar
• D.E. Ferreyra, V. Orquera, and N. Thome, A weak group inverse for rectangular matrices, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), 3727–3740. doi: 10.1007/s13398-019-00674-9
   Web of Science ®Google Scholar
• Y. Gao and J. Chen, Pseudo core inverses in rings with involution, Commun. Algebra 46(1) (2018), 38–50. doi: 10.1080/00927872.2016.1260729
   Web of Science ®Google Scholar
• W. Jiang and K. Zuo, Further characterizations of the -weak group inverse of a complex matrix, AIMS Mathematics 7(9) (2022), 17369–17392. doi: 10.3934/math.2022957
   Web of Science ®Google Scholar
• Y.Y. Ke, L. Wang, and J.L. Chen, The core inverse of a product and 2 × 2 matrices, Bull. Malays. Math. Sci. Soc. 42(1) (2019), 51–66. doi: 10.1007/s40840-017-0464-1
   Web of Science ®Google Scholar
• I. Kyrchei, Determinantal representations of the core inverse and its generalizations with applications, Journal of Mathematics 2019 (2019), Article ID 1631979. doi: 10.1155/2019/1631979
   Web of Science ®Google Scholar
• N. Liu and H. Wang, The characterizations of WG matrix and its generalized Cayley-Hamilton theorem, Journal of Mathematics 2021 (2021), Article ID 4952943.
   Web of Science ®Google Scholar
• X. Liu and N. Cai, High-order iterative methods for the DMP inverse, Journal of Mathematics 2018 (2018), Article ID 8175935.
   PubMedGoogle Scholar
• S.B. Malik and N. Thome, On a new generalized inverse for matrices of an arbitrary index, Appl. Math. Comput. 226 (2014), 575–580.
   Web of Science ®Google Scholar
• D. Mosić, Weighted gDMP inverse of operators between Hilbert spaces, Bull. Korean Math. Soc. 55 (2018), 1263–1271.
   Web of Science ®Google Scholar
• D. Mosić, New generalizations of the core and dual core inverses, Publ. Math. Debrecen, to appear.
   Google Scholar
• D. Mosić and P.S. Stanimirović, Representations for the weak group inverse, Appl. Math. Comput. 397 (2021), 125957.
   Web of Science ®Google Scholar
• D. Mosić, P.S. Stanimirović, and L.A Kazakovtsev, Application of m-weak group inverse in solving optimization problems, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 118 (2024), 13. doi: 10.1007/s13398-023-01512-9
   Web of Science ®Google Scholar
• D. Mosić and D. Zhang, Weighted weak group inverse for Hilbert space operators, Front. Math. China 15 (2020), 709–726. doi: 10.1007/s11464-020-0847-8
   Web of Science ®Google Scholar
• D. Mosić and D. Zhang, New representations and properties of -weak group inverse, Results Math. 78 (2023), 97. doi: 10.1007/s00025-023-01878-7
   Web of Science ®Google Scholar
• D. Mosić, D. Zhang, and P.S. Stanimirović, An extension of the MPD and MP weak group inverses, Appl. Math. Comput. 465 (2024), 128429.
   Web of Science ®Google Scholar
• K.M. Prasad and K.S. Mohana, Core-EP inverse, Linear Multilinear Algebra 62(6) (2014), 792–802. doi: 10.1080/03081087.2013.791690
   Web of Science ®Google Scholar
• C. Wang, X. Liu, and H. Jin, The MP weak group inverse and its application, Filomat 36(18) (2022), 6085–6102. doi: 10.2298/FIL2218085W
   Web of Science ®Google Scholar
• H. Wang, Core-EP decomposition and its applications, Linear Algebra Appl. 508 (2016), 289–300. doi: 10.1016/j.laa.2016.08.008
   Web of Science ®Google Scholar
• H. Wang and J. Chen, Weak group inverse, Open Mathematics 16 (2018), 1218–1232. doi: 10.1515/math-2018-0100
   Web of Science ®Google Scholar
• H.X. Wang, J. Gao, and X. Liu, The WG inverse and its application in a constrained matrix approximation problem, ScienceAsia 49(3) (2023), 361–368. doi: 10.2306/scienceasia1513-1874.2023.001
   Web of Science ®Google Scholar
• H. Wang and X. Liu, The weak group matrix, Aequationes Math. 93 (2019), 1261–1273. doi: 10.1007/s00010-019-00639-8
   Web of Science ®Google Scholar
• H. Yan, H. Wang, K. Zuo, and Y. Chen, Further characterizations of the weak group inverse of matrices and the weak group matrix, AIMS Mathematics 6(9) (2021), 9322–9341. doi: 10.3934/math.2021542
   Web of Science ®Google Scholar
• K. Zhang, X. Liu, and H. Jin, 1WG inverse of square matrices, Filomat, to appear.
   Google Scholar
• M. Zhou and J. Chen, Integral representations of two generalized core inverses, Appl. Math. Comput. 333 (2018), 187–193.
   Web of Science ®Google Scholar
• M. Zhou, J. Chen, and Y. Zhou, Weak group inverses in proper ∗-rings, J. Algebra Appl. 19(12) (2020), 2050238. doi: 10.1142/S0219498820502382
   Web of Science ®Google Scholar
• Y. Zhou, J. Chen, and M. Zhou, m-weak group inverses in a ring with involution, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115 (2021), 2. doi: 10.1007/s13398-020-00932-1
   Web of Science ®Google Scholar
• H. Zhu, On DMP inverses and m-EP elements in rings, Linear Multilinear Algebra 67(4) (2019), 756–766. doi: 10.1080/03081087.2018.1432546
   Web of Science ®Google Scholar
• H. Zou, J.L. Chen, and P. Patrício, Reverse order law for the core inverse in rings, Mediterr. J. Math. 15 (2018), 145. doi: 10.1007/s00009-018-1189-6
   Web of Science ®Google Scholar