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A nonlinear complementarity problem in mathematical programming in Hilbert space

Published online by Cambridge University Press:  17 April 2009

Sribatsa Nanda  and
Sudarsan Nanda
Sribatsa Nanda
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela, Orissa, India.
Sudarsan Nanda
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela, Orissa, India.
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Abstract

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In this paper we prove the following existence and uniqueness theorem for the nonlinear complementarity problem by using the Banach contraction principle. If T: K → H is strongly monotone and lipschitzian with k2 < 2c < k2+1, then there is a unique y ∈ K, such that Ty ∈ K* and (Ty, y) = 0 where H is a Hilbert space, K is a closed convex cone in H, and K* the polar cone.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 2 , April 1979 , pp. 233 - 236
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Goffman, Casper, Pedrick, George, First course in functional analysis (Prentice/Hall of India, New Delhi, 1974).Google Scholar