Fenchel’s Duality Theorem for Nearly Convex Functions

We present an extension of Fenchel’s duality theorem by weakening the convexity assumptions to near convexity. These weak hypotheses are automatically fulfilled in the convex case. Moreover, we show by a counterexample that a further extension to closely convex functions is not possible under these hypotheses. The authors are grateful to the Associate Editor for helpful suggestions and remarks which improved the quality of the paper. The second author was supported by DFG (German Research Foundation), project WA 922/1.