论文标题
通过分数演算
Jensen-type inequalities for convex and $m$-convex functions via fractional calculus
论文作者
论文摘要
不平等在纯数学和应用数学中起着重要作用。特别是，詹森（Jensen）的不平等是最著名的不平等之一，在研究差分方程的初始和边界价值问题的存在和独特性中起着主要作用。在这项工作中，我们证明了一些新的Jensen型不平等现象，用于$ M $ -CONVEX功能，并将其应用于广义的Riemann-Liouville-type Integral Operators。值得注意的是，如果我们考虑$ M = 1 $，我们会获得凸功能的新不平等。
Inequalities play an important role in pure and applied mathematics. In particular, Jensen's inequality, one of the most famous inequalities, plays a main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. In this work we prove some new Jensen-type inequalities for $m$-convex functions, and we apply them to generalized Riemann-Liouville-type integral operators. It is remarkable that, if we consider $m=1$, we obtain new inequalities for convex functions.
