Functional Equation In non-Archimedean Spaces Research Articles

On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean Spaces

On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean Spaces

Fixed point approach to the stability of a cubic and quartic mixed type functional equation in non-archimedean spaces

Fixed point approach to the stability of a cubic and quartic mixed type functional equation in non-archimedean spaces

Asymptotic Stability of the Pexider–Cauchy Functional Equation in Non-Archimedean Spaces

In this paper, we investigated the asymptotic stability behaviour of the Pexider–Cauchy functional equation in non-Archimedean spaces. We also showed that, under some conditions, if ∥f(x+y)−g(x)−h(y)∥⩽ε, then f,g and h can be approximated by additive mapping in non-Archimedean normed spaces. Finally, we deal with a functional inequality and its asymptotic behaviour.

The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),wherefmaps from an additive group to a complete non-Archimedean normed space.

On Hyers–Ulam stability of two functional equations in non-Archimedean spaces

In this paper we prove, using the fixed point method, the generalized Hyers–Ulam stability of two functional equations in complete non-Archimedean normed spaces. One of these equations characterizes multi-Cauchy–Jensen mappings, and the other gives a characterization of multi-additive-quadratic mappings.

Ulam–Hyers stabilities of a generalized composite functional equation in non-Archimedean spaces

AbstractIn this paper, we introduce a new generalized composite functional equation and prove its Hyers–Ulam–Rassias stability, Ulam–Găvruta–Rassias stability and Ulam–J. Rassias stability in non-Archimedean normed spaces using a fixed point method.

Stability of a Quartic Functional Equation

We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x − my) = 2(7m − 9)(m − 1)f(x) + 2m 2(m 2 − 1)f(y)−(m − 1)2 f(2x) + m 2{f(x + y) + f(x − y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces.

A General System of Nonlinear Functional Equations in Non-Archimedean Spaces

In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of functional equations, called general system of nonlinear functional equations, in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces.

Orthogonal Stability of an Additive-quartic Functional Equation in Non-Archimedean Spaces

Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equation \begin{align} f(2x+y)+ f(2x-y)&=4 f(x+y)+ 4 f(x-y) \nonumber & + 10 f(x) + 14f(-x) - 3 f(y)-3f(-y)\nonumber \end{align} for all $x, y$ with $x\perp y$, in non-Archimedean Banach spaces. Here $\perp$ is the orthogonality in the sense of Ratz.

Solution and stability of generalized mixed type additive and quadratic functional equation in non-Archimedean spaces

In this paper, we achieve the general solution and the generalized Hyres–Ulam–Rassias stability of the following additive–quadratic functional equation $$f (x + ky) + f (x - ky) = f (x + y) + f (x - y) + \frac{2(k + 1)}{k} f (ky) - 2(k + 1)f (y)$$ for fixed integers k with k ≠ 0, ±1 in non-Archimedean spaces.

On the stability of pexider functional equation in non-archimedean spaces

In this paper, the Hyers-Ulam stability of the Pexider functional equation in a non-Archimedean space is investigated, where σ is an involution in the domain of the given mapping f.MSC 2010:26E30, 39B52, 39B72, 46S10

Generalized Hyers-Ulam Stability of the Pexiderized Cauchy Functional Equation in Non-Archimedean Spaces

AbstractWe prove the generalized Hyers-Ulam stability of the Pexiderized Cauchy functional equation "Equation missing" in non-Archimedean spaces.

Functional Inequalities Associated with Cauchy Additive Functional Equation in Non-Archimedean Spaces

We investigate the generalized Hyers-Ulam stability of the functional inequalities∥f((x+y+z)/4)+f((3x−y−4z)/4)+f((4x+3z)/4)∥≤∥2f(x)∥and∥f((y−x)/3)+f((x−3z)/3)+f((3x+3z−y)/3)∥≤∥f(x)∥in non-Archimedean normed spaces in the spirit of the Th. M. Rassias stability approach.

Stability of a mixed type cubic–quartic functional equation in non-Archimedean spaces

In this paper, we prove the Hyers–Ulam–Rassias stability of the mixed type cubic–quartic functional equation f ( x + 2 y ) + f ( x − 2 y ) = 4 ( f ( x + y ) + f ( x − y ) ) − 24 f ( y ) − 6 f ( x ) + 3 f ( 2 y ) in non-Archimedean normed spaces.

AQCQ-Functional Equation in Non-Archimedean Normed Spaces

We prove the generalized Hyers-Ulam stability of generalized mixed type of quartic, cubic, quadratic and additive functional equation in non-Archimedean spaces.

Stability of Cubic and Quartic Functional Equations in Non-Archimedean Spaces

We prove generalized Hyers-Ulam–Rassias stability of the cubic functional equation f(kx+y)+f(kx−y)=k[f(x+y)+f(x−y)]+2(k 3−k)f(x) for all $k\in \Bbb{N}$ and the quartic functional equation f(kx+y)+f(kx−y)=k 2[f(x+y)+f(x−y)]+2k 2(k 2−1)f(x)−2(k 2−1)f(y) for all $k\in \Bbb{N}$ in non-Archimedean normed spaces.

Stability of Two Types of Cubic Functional Equations in Non-Archimedean Spaces

We prove the generalized stability of the cubic type functional equation $$f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)$$ and another functional equation $$f(ax+y)+f(x+ay)=(a+1)(a-1)^{2}[f(x)+f(y)] +a(a+1)f(x+y),$$ where $a$ is an integer with $a \neq 0, \pm 1$ in the framework of non-Archimedean normed spaces.

Stability of functional equations in non-Archimedean spaces

We prove the generalized Hyers-Ulam stability of the Cauchy functional equation f(x+y) = f(x)+f(y) and the quadratic functional equation f(x+ y) f(x - y) = 2f(x) + 2f(y) in non-Archimedean normed spaces.