Zi WANG , Yuwen WANG . A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES[J]. Acta mathematica scientia, Series B, 2017 , 37(6) : 1619 -1631 . DOI: 10.1016/S0252-9602(17)30095-4

[1] Cazassa P G, Christensen O. Perturbation of operators and applications to frame theory. J Fourier Anal Appl, 1997, 3(5):543-557[2] ChristensenO. Operators with closed range, pseudo-inverses, and pertyrbation of frame for a subspaces. Can Math Bull, 1999, 42(1):37-45[3] Nashed M Z, Chen X J. Convergence of Newton-like method for singular operator equations using outer inverse. Number Math, 1993, 66(2):235-257[4] Ma J P. A generalized transversility in global analysis. Pacific J Math, 2008, 236(2):101-115[5] Ma J P. (1, 2)-inverse of operators between Banach spaces and local conjugacy theorem. Chinese Ann Math Ser B, 1999, 20(1):57-62[6] Chen G L, Wei M S, Xue Y F. Perturbation analysis of the least square solution in Hilbert spaces. Linear Algebra Appl, 1996, 244:69-81[7] Chen G L, Xue Y F. Perturbation analysis for the operator equation Tx=b Banach spaces. J Math Anal Appl, 1997, 212:107-125[8] Kato T. Perturbation Theory for Linear Operator. Berlin:Springer-Verlag, 1984[9] Ding J. Perturbation of systems of linear algebraic equations. Linear Multilinear Algebra, 2000, 47:119-127[10] Ding J, Huang L. Perturbation of generalized inverse in Hilbert spaces. J Math, Anal Appl, 1996, 198:506-515[11] Huang Q L, Ma J P. Perturbation analysis of generalized inverses of linear operators in Banach spaces. Linear Algebra Appl, 2004, 289:355-364[12] Ma H F, Sun Sh, Wang Y W, Zhang W J. Perturbation of Moore-Penrose metric generalized inverse of linear operators in Banach spaces. Acta Math Sin, English Series, 2014, 30(7):1109-1124[13] Wei Y M, Chen G L. Perturbation analysis of least squares problem in Hilbert spaces. Appl Math Comput, 2001, 121:177-183[14] Wang Y W, Zhang H. Perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces. Linear Algebra Appl, 2007, 426:1-11[15] Huang Q L. On perturbations for oblique projection generalized inverses of closed linear operators in Banach spaces. Linear Algebra Appl, 2011, 434:2468-2474[16] Wang H, Wang Y W. Metric generalized inverse of linear operator in Banach spaces. Chin Ann Math, 2003, 24B(4):509-520[17] Ding J. New Perturbation results on pseudo-inverse of linear operators in Banach spaces. Linear Algebra Appl, 2003, 362:229-235[18] Yang X, Wang Y. Some new perturbation theorems for generalized inverses of linear operators in Banach spaces. Linear Algebra Appl, 2010, 433:1939-1949[19] Bai X Y, Wang X Y, et al. Definition and criterion of homogeneous generalized inverse. Acta Math Sin (Chin Ser), 2009, 52(2):353-360[20] Nashed M Z, Votruba G F. A unified approch to generalized inverses of linear operators:Ⅱ, extremal and proximal properties. Bull Amer Math Soc, 1982, 80(5):831-835[21] Barbu V Th. Precpuanu:Convexity and Optimization in Banach Spaces. Third ed. Dordrecht, Boston, Lancaster:Editura Academiei and D Reidel Publ Co, 1986[22] Deutsch F. Linear seletions for the metric projection. J Funct Anal, 1982, 49:269-292[23] Wang Y W. The Generalized Inverse Theorem and Its Application for Operator in Banach Spaces (in Chinese). Beijing:Science Press, 2005[24] Zheng W J, Ma H F, Wang Y W. A note of some perturbation theorems of metric generalized inverses in Banach spaces. Mathematics in Practice and Theory (In Chinese), 2016, 46(2):278-283[25] Nashed M Z, Ed. Generalized Inverse and Applications. New York/London:Academic Press, 1976[26] Wang H, Wang Y W. Generalized orthogonal decomposition theorem and generalized orthogonal complemented subspaces in Banach spaces. Acta Math Sin Chin Series, 2001, 44(6):1045-1050[27] Wang Y W, Yu J F. The character and representive of class of metric projection in Banach space. Acta Math Sci, 2001, 21(1):29-35