Dragomir, S. S. On Hadamard’s inequality on a disk. (English) Zbl 0948.26012 JIPAM, J. Inequal. Pure Appl. Math. 1, No. 1, Paper No. 2, 11 p. (2000). The following Hadamard-type inequalities for a convex function of two variables is offered: Let \(D= D(C,r)\) be a disc centered at the point \(C\) and having radius \(r>0\) in the plane. If \(f:D\to \mathbb{R}\) is convex on \(D\) then \[ f(C)\leq{1\over \pi r^2} \iint_D f(x,y) dx dy\leq {1\over 2\pi r} \int_L f(\gamma) d\ell(\gamma), \] where \(L\) is the circle centered at \(C\) with radius \(r\). Some mappings connected with this inequality and related results are also obtained. Reviewer: József Sándor (Cluj-Napoca) Cited in 1 ReviewCited in 19 Documents MSC: 26D15 Inequalities for sums, series and integrals 26B25 Convexity of real functions of several variables, generalizations Keywords:convex functions of two arguments; Jensen’s inequality; Hadamard’s inequality PDFBibTeX XMLCite \textit{S. S. Dragomir}, JIPAM, J. Inequal. Pure Appl. Math. 1, No. 1, Paper No. 2, 11 p. (2000; Zbl 0948.26012) Full Text: EuDML