ABSTRACT This paper presents an application of dissipative concept for stability analysis of continuous-time system with two additive time-varying delays in the state. Our attention is focused on analysis of whether the continuous-time system with two additive time-varying delays in the state is asymptotically stable and dissipative. By exploiting LyapunovKrasovski functional and introducing fr...

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem t...

We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for...

We deal with a conditional functional inequality x ⊥ y ⇒ ‖ f (x + y)− f (x)− f (y) ‖ ≤ (‖ x‖ + ‖ y‖ ), where ⊥ is a given orthogonality relation, is a given nonnegative number, and p is a given real number. Under suitable assumptions, we prove that any solution f of the above inequality has to be uniformly close to an orthogonally additive mapping g, that is, satisfying the condition x ⊥ y ⇒ g(...

The Brunn-Minkowski inequality gives a lower bound on the Lebesgue measure of a sumset in terms of the measures of the individual sets. This inequality plays a crucial role in the theory of convex bodies and has many interactions with isoperimetry and functional analysis. Stability of optimizers of this inequality in one dimension is a consequence of classical results in additive combinatorics....

The stability problem of functional equations was originated from a question of Ulam [66] concerning the stability of group homomorphisms: Let (G1, .) be a group and let (G2, ∗) be a metric group with the metric d(., .). Given ε > 0, does there exist a δ > 0, such that if a mapping h : G1 → G2 satisfies the inequality d(h(x1.x2), h(x1) ∗ h(x2)) < δ for all x1, x2 ∈ G1, then there exists a homom...

In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam stability of the new generalized mixed type additive and quadratic functional equation in fuzzy normed space. Mathematics Subject Classification 39B55, 39B52, 39B82

In this paper, the problem of stability criteria of neural networks (NNs) with two-additive time-varying delay compenents is investigated. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay stability criteria for NNs with two-additive time-...

In this article, we prove the generalized Hyers–Ulam stability of the following Cauchy additive functional equation

in this paper, using the fixed point and direct methods, we prove the generalized hyers-ulam-rassias stability of the following cauchy-jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. the concept of hyers-ulam-rassias stability originated from th. m. rassias’ stability theorem t...