SOC Means and SOC Inequalities

  • Jein-Shan ChenEmail author
Part of the Springer Optimization and Its Applications book series (SOIA, volume 143)


In this chapter, we present some other types of applications of the aforementioned SOC-functions, SOC-convexity, and SOC-monotonicity. These include so-called SOC means, SOC weighted means, and a few SOC trace versions of Young, Hölder, Minkowski inequalities, and Powers–Størmer’s inequality. We believe that these results will be helpful in convergence analysis of optimizations involved with SOC. Many materials of this chapter are extracted from [36, 77, 78], the readers can look into them for more details.

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsNational Taiwan Normal UniversityTaipeiTaiwan

Personalised recommendations