Ostrowski, Grüss, Čebyšev type inequalities for functions whose second derivatives belong to and whose modulus of second derivatives are convex.
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Lafforgue has proposed a new approach to the principle of functoriality in a test case, namely, the case of automorphic induction from an idele class character of a quadratic extension. For technical reasons, he considers only the case of function fields and assumes the data is unramified. In this paper, we show that his method applies without these restrictions. The ground field is a number field or a function field and the data may be ramified.