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A property of the convolution of two \(\varphi\)-convex functions. (English) Zbl 1073.26008

Summary: The convolution of two \(\varphi\)-convex functions is estimated by means of an inequality of Hadamard type. The sharpness of this inequality is discussed. As consequence, some inequalities for the convolution of two classically convex functions are obtained, providing us with a possibility of comparing the convolution product of two functions with their ordinary product, in the case of a class of convex functions.

MSC:

26A51 Convexity of real functions in one variable, generalizations
39B62 Functional inequalities, including subadditivity, convexity, etc.
26D15 Inequalities for sums, series and integrals
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