Quantitative Analysis for Perturbed Abstract Inequality Systems in Banach Spaces

Using the error bound results established in the present paper for approximate solutions, we study the stability issues when perturbed by possibly nonaffine smooth maps $E$ for the abstract inequality system $F\ge _K0$ defined by a (possible nonclosed) convex cone $K$ and a Frechet differentiable function $F$ satisfying the (extended) weak $\gamma$-condition. We provide some sufficient conditions, in terms of the information at a solution $x_0$, for ensuring the lower semicontinuity and/or the Lipschitz-like continuity at $x_0$ of the solution mapping for the perturbed system $F+E\ge _K0$ with smooth perturbation $E$. Explicit upper bounds of the Lipschitz-like moduli are also provided.

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