In this chapter, by using the orthogonally fixed point method, we prove Hyers–Ulam stability and hyperstability of 3-Lie homomorphisms for additive ρ-functional equation in algebras. Indeed, investigate system functional equations $$\displaystyle \begin{array}{@{}rcl@{}} \left \{ \begin {array}{ll} f(x+y)-f(x)-f(y)= \rho (2f\left (\frac {x+y}{2}\right )+ f(x)+ f(y)\right ),\\ f([[u,v],w])=[[f(u...

The specific force equation has many applications in open channel flow problems. Quantifying of the hydraulic jump phenomenon is an important application of this equation. This equation has a direct solution only for the rectangular channels. The trial and error procedure as well as the graphical solution are the existing methods of solving hydraulic jump equations. No direct solutions are avai...

In this work, we introduce a new type of generalised quartic functional equation and obtain the general solution. We then investigate stability results by using Hyers method in modular space for equations without Fatou property, ?b-condition both property. Moreover, with help fixed-point technique involving idea property spaces. Furthermore, suitable counter example is also demonstrated to prov...