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An existence theorem for the generalized complementarity problem

Published online by Cambridge University Press:  17 April 2009

J. Parida  and
B. Sahoo
J. Parida
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela, Orissa, India.
B. Sahoo
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela, Orissa, India.
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Abstract

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Given a closed, convex cone S, in Rn, its polar S* and a mapping g from Rn into itself, the generalized nonlinear complementarity problem is to find a z ∈ Rn such that

Many existence theorems for the problem have been established under varying conditions on g. We introduce new mappings, denoted by J(S)-functions, each of which is used to guarantee the existence of a solution to the generalized problem under certain coercivity conditions on itself. A mapping g:S → Rn is a J(S)-function if

imply that z = 0. It is observed that the new class of functions is a broader class than the previously studied ones.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 1 , August 1978 , pp. 51 - 58
Copyright
Copyright © Australian Mathematical Society 1979

References

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