NCP-functions play an important role in nonlinear complementarity problems(NCP). In this paper, we recall some definitions and properties of NCP-functions such as generalized Fisher-Burmeister function, ϕpFB(a; b) = ∥(a; b)∥p 􀀀 (a + b), and the generalized Natural-Residual function, ϕpNR(a; b) = ap􀀀(a􀀀b)p+: We attempt to generalize Natural-Residual function as a new NCP-function: ~ϕpNR(a; b) = (a + b)p 􀀀 ja 􀀀 bjp:

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