Fixed point of polynomial type nonlinear operators
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A concept of generalized polynomial operators is considered, and a fixed-point problem with these operators is posed. The existence of a fixed point, with a minimum norm property, is stated and a power series representation is obtained. Problems of this kind appear, for instance, in some two-point boundary-value problems in optimal control.
Key WordsPolynomial operators nonlinear equations fixed points contraction mapping principle successive approximation
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- 1.Halme, A., Orava, J., andBlomberg, H.,Polynomial Operators in Nonlinear Systems Theory, International Journal of Systems Science, Vol. 2, No. 1, 1971.Google Scholar
- 2.Halme, A., andOrava, J.,Generalized Polynomial Operators for Nonlinear Systems Analysis, IEEE Transactions on Automatic Control, Vol. AC-17, No. 2, 1972.Google Scholar
- 3.Halme, A.,Polynomial Operators for Nonlinear Systems Analysis, Acta Polytechnica Scandinavica, Series Ma, No. 24, 1972.Google Scholar
- 4.Balakrishnan, A. V.,A General Theory of Nonlinear Estimation Problems in Control Systems, Journal of Mathematical Analysis and Applications, Vol. 8, No. 1, 1964.Google Scholar
- 5.Falb, P. L., andDe Jong, J. L.,Some Successive Approximation Methods in Control and Oscillation Theory, Academic Press, New York, New York, 1969.Google Scholar
- 6.Athans, M., andFalb, P. L.,Optimal Control: An Introduction to the Theory and its Applications, McGraw-Hill Book Company, New York, New York, 1966.Google Scholar
- 7.Dieudonné, J. A.,Foundations of Modern Analysis, Academic Press, New York, New York, 1960.Google Scholar
- 8.Orava, J., andHalme, A.,Inversion of Generalized Power Series Representation (to appear).Google Scholar