On the Jensen convex and Jensen concave envelopes of means
Abstract In recent papers, the convexity of quasiarithmetic means was characterized under twice differentiability assumptions. One of the main goals of this paper is to show that the convexity or concavity of a quasiarithmetic mean implies the twice continuous differentiability of its generator. As a consequence of this result, we can characterize those quasiarithmetic means which admit a lower convex and upper concave quasiarithmetic envelope.
1999 ◽
Vol 14
(11)
◽
pp. 1089-1098
◽
Keyword(s):
2020 ◽
Vol 484
(1)
◽
pp. 123700
2012 ◽
Vol 16
(1)
◽
pp. 147-147