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In this article, we study the Hyers-Ulam stability of Davison functional equation f(xy)+f(x+y)=f(xy+x)+f(y)f\left(xy)+f\left(x+y)=f\left(xy+x)+f(y) on some unbounded restricted domains. Using the obtained results, we study an interesting asymptotic behavior of Davison functions. We also investigate the Hyers-Ulam stability of Davison functional equation and its generalized form given by f(xy)+g(x+y)=h(xy+x)+k(y),f\left(xy)+g\left(x+y)=h\left(xy+x)+k(y), for x,y∈R⩾0={t∈R:t⩾0}x,y\in {{\mathbb{R}}}^{\geqslant 0}=\left\{t\in {\mathbb{R}}:t\geqslant 0\right\}.

This article presents the general solution f:G→Vf:{\mathcal{G}}\to {\mathcal{V}} of the following functional equation: f(x)−4f(x+y)+6f(x+2y)−4f(x+3y)+f(x+4y)=0,x,y∈G,f\left(x)-4f\left(x+y)+6f\left(x+2y)-4f\left(x+3y)+f\left(x+4y)=0,\hspace{1.0em}x,y\in {\mathcal{G}}, where (G,+)\left({\mathcal{G}},+) is an abelian group and V{\mathcal{V}} is a linear space. We also investigate its Hyers-Ulam stability on some restricted domains. We apply the obtained results to present some asymptotic behaviors of this functional equation in the framework of normed spaces. Finally, we provide some characterizations of inner product spaces associated with the mentioned functional equation.

In this paper, we study the Ulam stability and hyperstability of a functional equation in m-Banach spaces. Multi-additive and multi-Jensen functions are particular cases of this functional equation. We also improve the main result of [Ciepli'nski, K. On Ulam Stability of a Functional Equation. Results Math. 2020, 75, Paper No. 151, 11 pp.] and its consequences. [ABSTRACT FROM AUTHOR]

In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation:ϕ(st−uv)+ϕ(sv+tu)=[ϕ(s)+ϕ(u)][ϕ(t)+ϕ(v)]\phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v)]by using the direct method and the fixed point method.

In this work, the Hyers-Ulam type stability and the hyperstability of the functional equationare proved.

In this paper, we present the general solution of two Pexiderized functional equations of Davison type without assuming any regularity assumption on the unknown functions. [ABSTRACT FROM AUTHOR]

In this paper, we study the Ulam stability and hyperstability of two general functional equations in several variables in 2-Banach spaces. Multi-additive and multi-Jensen functions are particular cases of these functional equations. We also improve the main results of Theorem 3 and Theorem 4 of [Ciepli'nski, K. Ulam stability of functional equations in 2-Banach spaces via the fixed point method. J. Fixed Point Theory Appl. 23 (2021), no. 3, Paper No. 33, 14 pp.] and their consequences. [ABSTRACT FROM AUTHOR]