Abstract In this paper, we unify the system of functional equations defining a multi-quadratic–cubic mapping to single equation. Applying fixed point theorem, study generalized Hyers–Ulam stability mappings. As result, investigate hyperstability mappings in some senses.

In this paper, we present our theoretical investigations of the technique of feedback error learning (FEL) from the viewpoint of adaptive control. We first discuss the relationship between FEL and nonlinear adaptive control with adaptive feedback linearization, and show that FEL can be interpreted as a form of nonlinear adaptive control. Second, we present a Lyapunov analysis suggesting that th...

In this paper, we introduce and solve a new general p-radical functional equation Also, investigate some stability hyperstability results for the considered in 2-Banach spaces. addition, prove of inhomogeneous

Abstract In this paper we give some hyperstability and stability results for the Cauchy Jensen functional equations on restricted domains. We provide a simple short proof Brzde?k’s result concerning equation.

In this paper, we prove the generalized Hyers-Ulam-Rassias stability for the Drygas functional equation$$f(x+y)+f(x-y)=2f(x)+f(y)+f(-y)$$ in Banach spaces by using the Brzc{d}ek's fixed point theorem. Moreover, we give a general result on the hyperstability of this equation. Our results are improvements and generalizations of the main result of M. Piszczek and J. Szczawi'{n}ska [21].

In this paper, we give some properties of the bi-Jensen functional equation and investigate its Hyers–Ulam stability hyperstability. We construct a function which is not continuous. Additionally, on restricted unbounded domains. Finally, apply obtained results to study interesting asymptotic behaviors functions.

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation$$fleft(sqrt[3]{ax^{3}+by^{3}}right)+fleft(sqrt[3]{ax^{3}-by^{3}}right)=2a^{2}f(x)+2b^{2}f(y),;; x,yinmathbb{R},$$for a mapping $f$ from $mathbb{R}$ into a vector space. We also investigate some stability and hyperstability results for...

For control of nonlinear sea plants such as ships and underwater vehicles nonlinear controllers based on artificial intelligence (fussy, neural, and neurofiizzy) are often introduced. They give a high control quality. Alas, it is very difficult or impossible to prove the stability for real systems with these controllers. Because technical regulations in many countries require stability proof be...