As is well known, equations of degree up to 4 can be solved in radicals . The solutions can be obtained, apart from the usual arithmetic operations, by the extraction of roots. In the case of the quadratic equation, this has a very concrete meaning. Even if the coefficients are arbitrary complex numbers, the solutions can always be calculated by the extraction of roots from nonnegative real num...

in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...

this paper presents some results concerning the existence of solutions for a functional integral equation of volterra type in two variables, via measure of noncompactness. two examples are included to illustrate the main result.

The result can be rephrased in geometric language to say that any projective cubic hypersurface defined over Q, of dimension at least 12, has a Q-point. Davenport’s result was extended to arbitrary number fields by Pleasants [9], and it would be interesting to know whether Theorem 1 could similarly be extended. These results can be seen as an attempt to extend the classical theorem of Meyer (18...

After introducing non-minimal variables, the midpoint insertion of Y Ȳ in cubic open Neveu-Schwarz string field theory can be replaced with an operator Nρ depending on a constant parameter ρ. As in cubic open superstring field theory using the pure spinor formalism, the operator Nρ is invertible and is equal to 1 up to a BRST-trivial quantity. So unlike the linearized equation of motion Y Ȳ QV ...

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

1. January 3rd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. Example 1: The Ohsawa–Takegoshi Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. Example 2: The Hörmander(-Skoda) Theorem . . . . . . ...

In this paper, we investigate the generalizedHyers--Ulam stability of the functional equation

The question about polynomial maps F : C → C, first raised by Keller [1] in 1939 for polynomials over the integers but now also raised for complex polynomials and, as such, known as The Jacobian Conjecture (JC), asks whether a polynomial map F with nonzero constant Jacobian determinant detF (x) need be a polyomorphism: Injective and also surjective with polynomial inverse. The known reductions ...