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A kind of generalized transversality theorem for $C^r$ mapping with parameter
1. | Department of Mathematics, Jilin University, Changchun, 130012, China |
2. | School of Science, Qiqihar University, Qiqihar, 161006, China |
The author considers a generalized transversality theorem of the mappings with parameter in infinite dimensional Banach space. If the mapping is generalized transversal to a single point set, and in the sense of exterior parameters, the mapping is a Fredholm operator, then there exists a residual set of parameter, such that the Fredholm operator is generalized transversal to the single point set.
References:
[1] |
K. C. Chang,
Methods in Nonlinear Analysis, Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2005. |
[2] |
J. P. Ma,
(1-2) Inverses of operators between banach spaces and local conjugacy theorem, Chinese Ann. Math. Ser. B, 20 (1999), 57-62.
doi: 10.1142/S0252959999000084. |
[3] |
J. P. Ma,
A generalized preimage theorem in global analysis, Sci. China. Ser. A, 44 (2001), 299-303.
doi: 10.1007/BF02878710. |
[4] |
J. P. Ma,
A generalized transversality in global analysis, Pacific J.Math., 236 (2008), 357-371.
doi: 10.2140/pjm.2008.236.357. |
[5] |
M. Z. Nashed,
Generalized Inverses and Applications, New York-San Francisco-London: Academic Pr. , 1976. |
[6] |
E. Zeidler,
Nonlinear Functional Analysis and its Applications, Springer Verlag, New York-Berline, 1988.
doi: 10.1007/978-1-4612-4838-5. |
show all references
References:
[1] |
K. C. Chang,
Methods in Nonlinear Analysis, Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2005. |
[2] |
J. P. Ma,
(1-2) Inverses of operators between banach spaces and local conjugacy theorem, Chinese Ann. Math. Ser. B, 20 (1999), 57-62.
doi: 10.1142/S0252959999000084. |
[3] |
J. P. Ma,
A generalized preimage theorem in global analysis, Sci. China. Ser. A, 44 (2001), 299-303.
doi: 10.1007/BF02878710. |
[4] |
J. P. Ma,
A generalized transversality in global analysis, Pacific J.Math., 236 (2008), 357-371.
doi: 10.2140/pjm.2008.236.357. |
[5] |
M. Z. Nashed,
Generalized Inverses and Applications, New York-San Francisco-London: Academic Pr. , 1976. |
[6] |
E. Zeidler,
Nonlinear Functional Analysis and its Applications, Springer Verlag, New York-Berline, 1988.
doi: 10.1007/978-1-4612-4838-5. |


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