Paper Title:

Boundness of the Power Exponential Function a^2b +b^2a

Author(s):

Yusuke Nishizawa, Yukuhito Yasuda

Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: ynishizawa@mail.saitama-u.ac.jp 

Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: y.yasuda.694@ms.saitama-u.ac.jp
 

Abstract:

In this paper, we consider the boundness of the power exponential function a^2b +b^2a for nonnegative real numbers a and b. The author proved that the function has the maximum value 1 for a + b = ½, but it is no known that the minimum value for a + b = ½. In this paper, we give the new proof of the function has the maximum value 1 and show that a^2b +b^2a > 0.989905 for a + b = ½.

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