The aim of this paper is to introduce $n$-variables mappings which are cubic in each variable and to apply a fixed point theorem for the Hyers-Ulam stability of such mapping in non-Archimedean normed spaces. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes are presented.

Abstract In this paper, we introduce a new quadratic functional equation and, motivated by equation, investigate n -variables mappings which are in each variable. We show that such can be unified as an namely, multi-quadratic equation. also apply fixed point technique to study the stability for equations. Furthermore, present example and few corollaries corresponding hyperstability outcomes.

The aim of this paper is to introduce and solve the following p-radical functional equation related quartic mappings. where f a mapping from R into vector space X p ≥ 3 an odd natural number. Using analogue version Brzd¸ek’s fixed point theorem [13], we establish some hyperstability results for considered in non-Archimedean Banach spaces. Also, give inhomogeneous mapping.

The scope of this research is to develop a hyperstable adaptive control system direct current (DC) drive speed for effective load torque attenuation. proposed controller based on the model reference framework and integrated into conventional DC cascade system. Its main features are as follows: (1) boundedness action signal, well armature loop non-stationarities, taken consideration with help he...

The aim of this note is to offer hyperstability results for linear functional equations of the form f(s) + f(t) = 1 n n ∑ i=1 f(sφi(t)) (s, t ∈ S), where S is a semigroup and where φ1, . . . , φn : S → S are pairwise distinct automorphisms of S such that the set {φ1, . . . , φn} is a group equipped with the composition as the group operation. The main results state that if f satisfies a stabili...

Inverse flexible dynamics control (IFDC) and fuzzy logic system adaptive control (FLSAC) strategies are used to track the end effector of a flexible space robot with sensors collocated at the joints, noncollocated at the end effector and 0.5m from the elbow joint on link 2. Collocated joint sensors satisfy hyperstability conditions but fail to capture nonminimum phase (NMP) response that genera...

In this paper a description of a certain class of multiloop systems, called the Standard Multiloop Form, is introduced. This description is expressed explicitly in terms of certain scalar subsystems and can be shown to include many of the common descriptions of multiloop systems. The stability criteria presented in this paper involve the individual Nyquist plots of the linear scalar subsystems ...

‎The aim of this paper is to introduce and solve the‎ radical cubic functional equation‎ ‎$‎‎fleft(sqrt[3]{x^{3}+y^{3}}right)+fleft(sqrt[3]{x^{3}-y^{3}}right)=2f(x)‎$.‎ ‎We also investigate some stability and hyperstability results for‎ ‎the considered equation in 2-Banach spaces‎.

Abstract We discuss some frequency-domain criteria for the exponential stability of nonlinear feedback systems based on Popov’s hyperstability theorem. The main results are new bounds convergence rates perturbations damped harmonic oscillator, including Hessian-damped case, when satisfy certain sectoriality or convexity hypotheses. also include a simplified proof theorem in its general form, wh...