| We study the stability of certain inequality systems that arise in monotonic analysis and are defined by certain classes of abstract linear functions. We consider the non-negative orthant R +n as a base space and the class of abstract linear functions consisting of the family of the max-type functions of the form a (x ):=‹ a, x › = max i=1,2,...,n a i x i , with a and x in R +n. The stability, under perturbations of all the coefficients, of the solution set mapping of systems of infinitely many max-type inequalities, { ‹ a t, x › ≥ b t, t ∈ T } is studied from different points of view (lower semicontinuity, continuity in the Bouligand sense, metric regularity, the existence of strong Slater points, adapted Robinson-Ursescu condition). Some Farkas and Gale type solvability results are also presented. |
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