The aim of this paper is to introduce and solve the following pradical functional equation related Drygas mappings f(?(p&x^p+ y^p ))+f(?(p&x^p+ ))=2f(x)+f(y)+f(-y),x,y ?R, where f a mapping from R into vector space X p ? 3 an odd natural number. Using analogue version Brzd?k’s fixed point theorem [14], we establish some hyperstability results for considered in non-Archimedean Banach spa...

The study of stability problems of functional equations was motivated by a question of S.M. Ulam asked in 1940. The first result giving answer to this question is due to D.H. Hyers. Subsequently, his result was extended and generalized in several ways.We prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=Ag(x)+Bg(y)on restricted domain. Namely, we show, under some weak natural...

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...

In this paper, we introduce $n$-variables mappings which are cubic in each variable. We show that such satisfy a functional equation. The main purpose is to extend the applications of fixed point method establish Hyers-Ulam stability for multi-cubic mappings. As consequence, prove equation can be hyperstable.

The hyperstability theory of adaptive control systems is extended to encompass plants with unmodelled dynamics and disturbances. The analysis not only shows that leakage in the adaptive law is a natural way to avoid robustness problems (which is a known result in adaptive control theory), but also provides a new adaptive law that is a sort of signal-dependent σ-modification. The proposed adapti...

The development of fuzzy control systems is usually performed by heuristic means, incorporating human skills, the drawback being in the lack of general-purpose development methods. A major problem, which follows from this development, is the analysis of the structural properties of the control system, such as stability, controllability and robustness. Here comes the first goal of the paper, to ...

Modern aircraft control systems contain the so-called rate limiter elements which are in fact incorporating the saturation function which is a bounded nonlinearity. In certain critical cases the so-called sector rotation a standard procedure in absolute stability leads to the fact that the sector conditions are broken outside a bounded domain. In order to apply standard results of the absolute ...