Nonlinear Problems and Hölder's Inequality

DOI Web Site 26 References Open Access
  • TANAKA Hisa-Aki
    Graduate School of Informatics and Engineering, University of Electro-Communications

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Other Title
  • 非線形問題とヘルダーの不等式

Description

Since the basis of Hölder's inequality was found by mathematicians, i.e., independently by Rogers in 1888 and Hölder in 1889, the inequality has been frequently utilized as a basic inequality in mathematical analysis such as functional analysis. However, surprisingly, no physical interpretation of the inequality was introduced until 2014. In this article, I show that the inequality gives an elegant solution to a recent open nonlinear problem. It is also asserted that the inequality can be a fundamental basis in Tsallis statistics, studied recently in information and communications technology. Furthermore, it is argued that the inequality can make a useful addition to modern control theory.

Journal

  • IEICE ESS Fundamentals Review

    IEICE ESS Fundamentals Review 9 (3), 219-228, 2016

    The Institute of Electronics, Information and Communication Engineers

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