in this paper, we prove the generalized hyers-ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-archimedean $mathcal{l}$-fuzzy normed spaces.

In order to derive the offset curves by using cubic Bézier curves with a linear field of normal vectors (the so-called LN Bézier curves) more efficiently, three methods for approximating degree n Bézier curves by cubic LN Bézier curves are considered, which includes two traditional methods and one new method based on Hausdorff distance. The approximation based on shifting control points is equi...

and Applied Analysis 3 is called a quadratic functional equation. In particular, every solution of the quadratic functional equation is said to be a quadratic mapping. A generalized Hyers-Ulam stability problem for the quadratic functional equation was proved by Skof 7 for mappings f : X → Y , where X is a normed space and Y is a Banach space. Cholewa 8 noticed that the theorem of Skof is still...

In this paper, we give three equivalent properties of the class of multivariate simple cubic natural exponential families (NEF’s). The first property says that the cumulant function of any basis of the family is a solution of some Monge-Ampère equation, the second is that the variance function satisfies a differential equation, and the third is characterized by the equality between two families...

Abstract Bezier is one of the influent polynomial and important tool for interpolation because it is easy to compute and is also very stable. In this paper, we develop very simpler constraints for Quadratic and Cubic Bezier curve which they ensure to constrained by a line. The end control points of the Quadratic and Cubic Bezier curve will be left on user desire and only middle control points o...

The three bilinearities uv, uv, uv for functions u, v : R2×[0, T ] 7−→ C are sharply estimated in function spaces Xs,b associated to the Schrödinger operator i∂t+∆. These bilinear estimates imply local wellposedness results for Schrödinger equations with quadratic nonlinearity. Improved bounds on the growth of spatial Sobolev norms of finite energy global-in-time and blow-up solutions of the cu...

We study the stability of standing-waves solutions to a scalar non-linear Klein–Gordon equation in dimension one with quadratic-cubic non-linearity. Orbits are obtained by applying semigroup generated negative complex unit multiplication on critical point energy constrained charge.