Abstract The presented work summarizes the relationships between stability results and separation theorems. We prove equivalence different types of theorems on by an additive map concerning Cauchy functional equation.

in this paper we use a class of stochastic functional kolmogorov-type model with jumps to describe the evolutions of population dynamics. by constructing a special lyapunov function, we show that the stochastic functional differential equation associated with our model admits a unique global solution in the positive orthant, and, by the exponential martingale inequality with jumps, we dis...

Luce and Marley [2005. Ranked additive utility representations of gambles: Old and new axiomatizations. Journal of Risk and Uncertainty, 30, 21–62] examined various relations between mathematical forms for the utility of joint receipt of gambles and for the utility of uncertain gambles. Their assumptions lead to a bisymmetry functional equation which, when the gambles are ranked, is defined on ...

in  this paper, we investigate the generalizedhyers-ulam-rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{z}-{0,pm1}$) in $p-$banach spaces.

The purpose of this paper is to solve the seventh-order functional equation as follows:  --------------------------- Next, we study the stability of this type of functional equation. Clearly, the function ----------  holds in this type functional equation. Also, we prove Hyers-Ulam stability for this type functional equation in the β-Gaussian Banach space.  

Abstract. A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y (t)) on (T × {1, 2} × R), where T is the twodimensional torus. Here (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance. Y (t) is an additive functional of K, define...

Let X,Y be Banach modules over a C∗-algebra and let r1, . . . , rn ∈ R be given. We prove the generalized Hyers-Ulam stability of the following functional equation in Banach modules over a unital C∗-algebra: ∑n j 1 f −rjxj ∑ 1≤i≤n,i / j rixi 2 ∑n i 1 rif xi nf ∑n i 1 rixi . We show that if ∑n i 1 ri / 0, ri, rj / 0 for some 1 ≤ i < j ≤ n and a mapping f : X → Y satisfies the functional equation...

If 1(t) is odd about several points (xe , I (x,)) it is to be understood that the exceptional set may depend on x a . BOAS 1) proves among others that if 1(t) is periodic, bounded on a set of positive measure, and satisfies (1) for a set of x's having positive measure then 1(t) is equivalent to a constant (i .e . 1(t) is constant almost everywhere) . He also shows there exists a bounded periodi...

This research paper focuses on the investigation of solutions ?:G?R maximum functional equation max{?(xy),?(xy?1)}=?(x)?(y), for every x,y?G, where G is any group. We determine that if a group divisible by two and three, then non-zero solution necessarily strictly positive; work Toborg, we can conclude are exactly e|?| an additive function ?:G?R. Moreover, our yields reliable to G, instead bein...