About Karamata Mean Value Theorem, Some Consequences and Some Stability Results

作者：Marinescu Dan Stefan^*; Monea Mihai; Mortici Cristinel

来源：Results in Mathematics, 2017, 72(1-2): 329-342.

DOI：10.1007/s00025-017-0680-x

• Karamata theorem
• continuous function
• both-sided differentiable function
• convex function
• monotone function
• integrable function
• stability

The aim of this paper is to explore Karamata's mean value theorem. In the second section, we reformulate a mean theorem for the convex functions and prove some consequences. Also, we prove an integral version of Karamta theorem. Third section is reserved to the stability results. We establish some conditions for the stability of the intermediate point arising from Karamata, Godner and the integral mean theorem proved in the previous section.

• 出版日期2017-9