Jakšetić Julije, Pečarić Josip, Smoljak Kalamir Ksenija
1Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia.
2Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia.
J Inequal Appl. 2018;2018(1):288. doi: 10.1186/s13660-018-1882-9. Epub 2018 Oct 22.
In this paper some Bellman-Steffensen type inequalities are generalized for positive measures. Using sublinearity of a class of convex functions and Jensen's inequality, nonnormalized versions of Steffensen's inequality are obtained. Further, linear functionals, from obtained Bellman-Steffensen type inequalities, are produced and their action on families of exponentially convex functions is studied.
本文将一些贝尔曼 - 施泰芬森型不等式推广到正测度情形。利用一类凸函数的次线性和詹森不等式，得到了施泰芬森不等式的非归一化形式。此外，由所得的贝尔曼 - 施泰芬森型不等式构造出线性泛函，并研究了它们对指数凸函数族的作用。
