Error bound and well-posedness with respect to an admissible function

Using techniques of variational analysis and in terms of subdifferential, we study the generalized error bound defined by an admissible function, an interesting extension of the Holder error bound and the usual error bound. With the help of a chain rule of subdifferential established in the paper, without the solvability assumption, we provide a sufficient condition for a nonconvex inequality to have a global generalized error bound. We also provide some sufficient and/or necessary conditions for an inequality to have Holder error bounds. As applications, we consider well-posedness with respect to an admissible function.