| point to the set involving the function that defines the set C with certain properties. Examples of such sets include the solution set of a functional inequality, the set of all minimizers or the set of stationary points. In this paper, we derive sufficient conditions for the existence of nonlinear functional error bounds for the solution set of an functional inequality and the set of subdifferential stationary points involving a lower semicontinuous function defined on a Banach space. It is also shown that error bound conditions for a functional inequality become necessary if the function is convex. Applying the error bound conditions to the set of all minimizers of the function, we obtain the conditions for the existence of the $\psi$-weak sharp minima. |
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