Stabilities of multiplicative inverse quadratic functional equations arising from Pythagorean means

Abstract

In this article, we propose advanced multiplicative inverse quadratic
mappings involving arguments in rational form. The motivation to introduce these functional equations is due to inverse square law arising in gravity, electricity and radiation. We obtain their solutions and prove their stabilities in the restricted domain and non-Archimedean fields. Moreover, we provide a suitable counterexample for the failure of stability results when critical case arises. We elucidate these equations with Pythagorean means.