Sensitivity of Solutions to a Parametric Generalized Equation

In the present paper we prove that, under some suitable conditions on multifunctions $C!: {I!!R}^lrightrightarrows {I!!R}^n$ , $F!:{I!!R}^dtimes {I!!R}^nrightrightarrows {I!!R}^m$ , and $K!:{I!!R}^ltimes {I!!R}^nrightrightarrows {I!!R}^m$ , the generalized perturbation multifunction $G!: {I!!R}^dtimes{I!!R}^ltimes {I!!R}^mrightrightarrows {I!!R}^n$ , of the form $$G(mu,lambda,nu)={xin C(lambda) | nuin F(mu,x)+K(lambda,x)},$$ is proto-differentiable at (μ, λ, ν) relative to x?∈?G(μ, λ, ν). Moreover, in a special case, where K(λ, x) is a normal cone to C(λ) at x, we also provide sufficient conditions for G(·) to be single-valued on a neighborhood of (μ, λ, ν) and semi-differentiable at (μ, λ, ν).