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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 6 > No. 1


Some Characterizations of Relatively Strictly Semi-Monotone (Semi-Monotone) Operators and Applications

PP: 75-81
Mohamed A. Tawhid,
In [M. A. Tawhid, On Characterization of E(E0)-Properties in Nonsmooth Functions. Applied Mathematics and Computation. 175: 2: pp. 1609-1618, April 15, (2006)], Tawhid gave characterization of strictly semi-monotone (semi-monotone) properties in nonsmooth functions that are H-differentiable. He showed the usefulness of his results to nonlinear complementarity problems. A natural question is: Can we extend these characterizations in order to apply the results to nonsmooth generlaized complementarity problems? This paper give an affirmative answer. We introduce the concepts of relatively semi-monotone and relatively strictly semi-monotone in order to give characterizations of the relatively semi-monotone and relatively strictly semi-monotone properties. Also, our results give characterizations of relatively P(P0)- when the underlying functions are C1-functions, semismoothfunctions, and locally Lipschitzian functions. Moreover, we show useful applications of our results by giving illustrations to nonsmooth generalized complementarity problems that admit the H-differentiability

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