in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

Medium Field Equation (MFE) multivariate public key cryptosystems were broken by High Order Linearization Equation (HOLE) attack. In order to avoid HOLE attack, we proposed an improvement of MFE, Cubic MFE public key encryption scheme. In our construction, multiplications of three second order matrices were used to get a set of cubic polynomials in the central map. Through theoretical analysis ...

In this paper we solve the inversion problem of the radiative transfer process in the isotropic plane-parallel atmosphere by iterative integrations of the Milne integral equation. As a result, we obtain the scattering function in the form of a cubic polynomial in optical thickness. The author has already solved the same problem by iterative integrations of Chandrasekhar’s integral equation. In ...

In this manuscript, we study the properties and equivalence results for different forms of quadratic functional equations. Using Brzdȩk Ciepliński fixed-point approach, investigate generalized Hyers–Ulam–Rassias stability 3-variables equation in setting 2-Banach space. Also, obtain some hyperstability equation. The obtained paper extend several known literature to

In a recent paper, Allanach et al introduced geometric method to solve the anomaly cancellation equations for $U(1)$ gauge theory with an arbitrary number of charges - Method Chords known in Diophantine analysis. We extend their result non-Abelian groups, and show that this can be used find general solution Standard Model group on curved background. Given $K$ $(\textbf{2}, \textbf{3})$, $L$ \te...

Hervé Leblond, David Kremer, and Dumitru Mihalache Laboratoire de Photonique d’Angers, Université d’Angers, 2 Bd. Lavoisier, 49045 Angers Cedex 01, France Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest, 077125, Romania Academy of Romanian Scientists, 54 Splaiul Independentei, Bucharest 050094, Romania Abstract By using a reduc...

In 1940 and 1964, Ulam proposed the general problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. In 1941, Hyers solved this stability problem for linear mappings. According to Gruber 1978 this kind of stability problems are of the particular interest in probability theory and in ...

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.