부산대학교 도서관

The authors introduced a new reciprocal second power functional equation $$ m_q\left(\frac{uv}{2u+v}\right)+m_q\left(\frac{uv}{2u-v}\right)=2m_q(u)+8m_q(v).\tag1 $$ They prove that $m_q\colon \Bbb{R}^*\to \Bbb{R}$ satisfies this functional equation if and only if there exists an identity function $I\colon \Bbb{R}^*\to\Bbb{R}$ such that $m_q(u)=[I(\frac{1}{u})]^2$ for all $u\in\Bbb{R}^*$. They investigate its various classical stability results in modular spaces with and without using Fatou property, and in $\beta$-homogenous spaces. They also associated equation (1) with Coloumb's law to employ it in various situations to connect the electrostatic forces of attraction in different assumptions.