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...

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 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...

Neuronal microtubules support intracellular transport, facilitate axon growth, and form a basis for neuronal morphology. While microtubules in nonneuronal cells are depolymerized by cold, Ca(2+), or antimitotic drugs, neuronal microtubules are unusually stable. Such stability is important for normal axon growth and maintenance, while hyperstability may compromise neuronal function in aging and ...

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 ...

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 ...

Preorganization is shown to endow a protein with extraordinary conformational stability. This preorganization is achieved by installing side-chain substituents that impose stereoelectronic and steric effects that restrict main-chain torsion angles. Replacing proline residues in (ProProGly)(7) collagen strands with 4-fluoroproline and 4-methylproline leads to the most stable known triple helices...