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On Convergence of Iterations for Fixed Points of Repulsive Type

Published online by Cambridge University Press:  20 November 2018

Rao S. Koneru  and
B. S. Lalli
Rao S. Koneru
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
B. S. Lalli
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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This paper deals with the convergence of iterations of the equation

1.1

with u0 ∊ Rn, both as a root and a point of repulsion. Here u and ϕ are real n-vectors and ϕ is continuously differentiate with respect to u. By taking u0 as an initial approximation to u0 in a neighbourhood of u0 we define the sequence of iterates {uk+1} by

1.1

For the sake of convenience we shall, sometimes, call the equation (1.1) an iteration.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 353 - 357
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Coddinton, E. A. and Levinson, N., Theory of ordinary differential equations, McGraw-Hill, New York, 1955.Google Scholar
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3. Apostol, T. M., Mathematical analysis, Addison-Wesley, Reading, Mass., 1964.Google Scholar