We present some Farkas-type results for inequality systems involving finitely many functions. Therefore we use a conjugate duality approach applied to an optimization problem with a composed convex objective function and convex inequality constraints. Some recently obtained results are rediscovered as special cases of our main result.

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The aim of the present paper is to provide a formula for the ε-subdifferential of f + g • h different from the ones which can be found in the existent literature. Further we equivalently characterize this formula by using a so-called closedness type regularity condition expressed by means of the epigraphs of the conjugates of the functions involved. Even more, using the ε-subdifferential formula we are able to derive necessary and sufficient conditions for the ε-optimal solutions of composed convex optimization problems.

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