Note on convex functions bounded on regular hypersurfaces

Abstract

Let Rn denote the Cartesian product of n copies.of. tlie space R of real numbers. A r e a l valued function <p defined on an open and convex subset A of Rn i s calle'd convex i f f theinequality (of Jensen) 9 (* + y ^ y ( ^ ) * y(y) holds f o r every pair (x,y)e A x A . M.Kuczma and the present author have introduced In [2] some set classes relevant to the notion of convex function (Fragment tekstu).