In this study, we propose a new rational functional equationJr((x+y)/2)=2Jr(x)Jr(y)/[Jr(x)+Jr(y)]and obtain its solution. We also investigate its various stabilities by a fixed point method

The analysis of stability results of different multiplicative inverse functional equations is an emerging trend in the research field of fundamental stability of equations emanated through the query of Ulam. This paper focuses on proving various classical stabilities of a new inverse fourth power functional equation connected with stability problems in the setting of fields that do not satisfy Archimedean property. The solution of the equation dealt in this study is interpreted with the intensity of scattered light and decay of radar energy in physics.