Two approaches for the stability of multi-radical sextic mappings

In the current investigation, we define a multi-radical sextic mapping by formulating it as a system of radical functional equations and subsequently presenting an equivalent unified functional equation. We prove the stability of multi-radical sextic mappings by employing the Hyers (direct) method and a fixed-point approach due to Brzdȩk. As direct consequences of our main results, we establish Hyers–Ulam stability of the mappings under consideration. Furthermore, by comparing the obtained Hyers stability estimates, we demonstrate that imposing the zero condition yields a sharper approximation bound than the corresponding result obtained without this condition.