Quadratic functional equations
Fuzzy Stability of Quadratic Functional Equations
... additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et ...following quadratic functional equations fxy ...
16
Quadratic functional equations of Pexider type
... the functional equation (1.5) which is a “pexiderized” form of the quadratic functional equation ...the quadratic functional equations of Pexider type, ...
9
Stability of quadratic functional equations in tempered distributions
... was proved by Skof []. Thereafter, many authors studied the stability problems of (.) in various settings (see [, , , ]). Usually, quadratic functional equations are used to characterize ...
11
Stability of Quadratic Functional Equations via the Fixed Point and Direct Method
... stability theorems of functional equations which generalize the Hyers’ result. In 1978, Rassias 6 attempted to weaken the condition for the bound of Cauchy difference controlled by a sum of unbounded ...
15
Stability of quadratic functional equations in generalized functions
... 7. Aczél, J, Dhombres, J: Functional Equations in Several Variables. Cambridge University Press, Cambridge (1989) 8. Skof, F: Local properties and approximation of operators. Rend. Semin. Mat. Fis. Milano ...
15
Refined stability of additive and quadratic functional equations in modular spaces
... of functional equations originated with Ulam [], who raised the stability problem of group ...Cauchy functional equation in Banach ...of functional equations may be called Hyers-Ulam ...
13
Approximate solution of generalized inhomogeneous radical quadratic functional equations in 2 Banach spaces
... for functional equations originates from a question of Ulam [28] concerning the stability of group ...of functional equations has been extensively investi- gated and generalized by many ...
13
On stability of functional equations related to quadratic mappings in fuzzy Banach spaces
... of functional equations was originally introduced by Ulam [] in ...linear functional equation of Banach ...Jensen functional and the quadratic functional ...
12
On the Stability of Functional Equations in Random Normed Spaces
... are said to be Jensen- Type Quadratic functional equations. In 2009, S.Y.Jang, Rye Lee, Choonkil Park, and Dong Yun Shin [24] proved the Fuzzy stability of equation (1.3) and (1.4). The notion of a ...
10
Generalized Ulam - Hyers Stability of on (AQQ): Additive - Quadratic - Quartic Functional Equation
... Keywords: Additive functional equations, Quadratic functional equations, Quartic functional equations, Mixed type functional equations, Ulam - Hyers stability, Ulam - Hyers - Rassias sta[r] ...
21
On the Ulam type stability of several types of quadratic fuzzy set valued functional equations
... these equations quadratic functional equations and every solution a quadratic function ...single-valued equations, the corresponding Ulam type stability of these equations ...
19
On approximate dectic mappings in non-Archimedean spaces: A fixed point approach
... During the last three decades theory of non-Archimedean spaces has gained the interest of physi- cists for their research, in particular the problems that emerge in quantum physics, p-adic strings and superstrings [21]. ...
12
General uniqueness theorem concerning the stability of additive, quadratic, and cubic functional equations
... In this section, let X and Y be real normed spaces and let V and W be real vector spaces. In the following theorem, we prove that if, for any given mapping f , there exists a mapping F (near f ) with some properties ...
12
Numerical simulation of continuity equations by evolving diffeomorphisms
... The 2D algorithm involves several pre- and post-processing steps, which present addi- tional challenges with respect to numerical accuracy and computational complexity. The proposed finite element discretization allows ...
25
Dhage iteration method for approximating positive solutions of quadratic functional differential equations
... on functional differential equations as far as Dhage iteration method is concerned for proving the existence and approxi- mation of the solutions on ...differential equations with past history occurs ...
13
Quadratic $alpha$-functional equations
... The functional equation f (x + y) = f (x) + f(y) is called the Cauchy equation. In particular, every solution of the Cauchy equation is said to be an additive mapping. Hyers [19] gave a first affirmative partial ...
9
On the generalized Hyers Ulam Rassias stability problem of radical functional equations
... for all x ∈ R. Letting n → ∞, we have the uniqueness of F(x). This completes the proof. Theorem . Let f : R → Y be a φ -approximatively radical quadratic function with f () = . Assume that the function φ is ...
13
A Ternary Quadratic Diophantine Equation $x^2+y^2=65z^2$
... ternary quadratic equations are rich in variety, one may search for the other choice of ternary quadratic Diophantine equations and determine their integer solutions along with suitable ...
7
Generalized Ulam-Hyers Stability of the Harmonic Mean Functional Equation in Two Variables
... [40] K. Ravi, J.M. Rassias and B.V. Senthil Kumar, Ulam stability of Reciprocal Difference and Adjoint Funtional Equations, The Australian J. Math. Anal.Appl. 8(1), Art.13 (2011), 1-18. [41] K. Ravi, J.M. Rassias ...
17
Orthogonal stability of mixed type additive and cubic functional equations
... f(x + y) = f (x) + f (y), (x, y ∈ A, x⊥y) (1.1) in which ⊥ is an abstract orthogonally was first investigated by S. Gudder and D. Strawther [7]. R. Ger and J. Sikkorska discussed the orthogonal stability of the equation ...
9