On the stability of a quadratic Jensen type functional equation

In this paper we obtain the general solution of the quadratic Jensen type functional equation

and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and G vruta.     

The generalized Hyers-Ulam-Rassias stability of a cubic functional equation

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability for a cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x).     

Stability of a mixed additive and cubic functional equation in quasi-Banach spaces

In this paper we establish the general solution and investigate the Hyers-Ulam-Rassias stability of the following functional equation

f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+2[f(2x)−2f(x)]     

Stability of a functional equation deriving from cubic and quadratic functions

In this paper we establish the general solution of the functional equation 6f(x+y)−6f(x−y)+4f(3y)=3f(x+2y)−3f(x−2y)+9f(2y) and investigate the Hyers-Ulam-Rassias stability of this equation.     

Stability of a functional equation deriving from quadratic and additive functions in quasi-Banach spaces

In this paper we establish the general solution of the functional equation

f(2x+y)+f(2x−y)=f(x+y)+f(x−y)+2f(2x)−2f(x)     

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

Stability of a mixed additive and quadratic functional equation in quasi-Banach spaces

We study the stability of functional equations in quasi-Banach spaces where the quasi-norm is not assumed to be a p-norm. To overcome the modulus of concavity greater than 1 and the discontinuity of quasi-norms we use the squeeze inequality presented in an explicit revision of Aoki–Rolewicz Theorem  [13, Theorem 1]. As illustrations, we prove an extension of the stability of a mixed additive and quadratic functional equation in p-Banach spaces to quasi-Banach spaces with better approximation. The technique may be used to prove extensions of other results on the stability of functional equations in p-Banach spaces to quasi-Banach spaces.     

Solution to Kim-Rassias's question on stability of generalized Euler-Lagrange quadratic functional equations in quasi-Banach spaces

By using Aoki-Rolewicz Theorem on p-normalizing a quasi-normed space, we prove stability results for Euler-Lagrange quadratic functional equations in quasi-Banach spaces. These results improve stability results and give the answer to Kim-Rassias's question.     

Approximation and solution of a general symmetric functional equation

In this paper, we investigate the Hyers–Ulam–Rassias stability of a general equation f(_φ1(x,y))=_φ2(f(x),f(y))$f\left({\phi }_1(x,y)\right)={\phi }_2(f\left(x\right),f\left(y\right))$ in metric spaces. As a consequence, we obtain some stability results in the sense of Hyers–Ulam–Rassias.     

Solution of the Ulam stability problem for Euler–Lagrange–Jensen k‐quintic mappings

In this paper, we are introducing pertinent Euler–Lagrange–Jensen type k‐quintic functional equations and investigate the ‘Ulam stability’ of these new k‐quintic functional mappings f:X→Y, where X is a real normed linear space and Y a real complete normed linear space. We also solve the Ulam stability problem for Euler–Lagrange–Jensen alternative k‐quintic mappings. Copyright © 2016 John Wiley & Sons, Ltd.     

On the stability of Euler-Lagrange type cubic mappings in quasi-Banach spaces

In this paper, we solve the generalized Hyers-Ulam-Rassias stability problem for Euler-Lagrange type cubic functional equations

f(ax+y)+f(x+ay)=(a+1)²(a−1)[f(x)+f(y)]+a(a+1)f(x+y)     

A class of impulsive nonautonomous differential equations and Ulam–Hyers–Rassias stability

In this paper, we study a model described by a class of impulsive nonautonomous differential equations. This new impulsive model is more suitable to show dynamics of evolution processes in pharmacotherapy than the classical one. We apply Krasnoselskii's fixed point theorem to obtain existence of solutions. Meanwhile, we mainly present the sufficient conditions on Ulam–Hyers–Rassias stability on both compact and unbounded intervals. Many analysis techniques are used to derive our results. Copyright © 2014 John Wiley & Sons, Ltd.     

Hyers–Ulam–Rassias stability of a generalized Apollonius–Jensen type additive mapping and isomorphisms between C *‐algebras

Let X, Y be Banach modules over a C *‐algebra. We prove the Hyers–Ulam–Rassias stability of the following functional equation in Banach modules over a unital C *‐algebra: It is shown that a mapping f: X → Y satisfies the above functional equation and f (0) = 0 if and only if the mapping f: X → Y is Cauchy additive. As an application, we show that every almost linear bijection h: A → B of a unital C *‐algebra A onto a unital C *‐algebra B is a C *‐algebra isomorphism when h (2^d uy) = h (2^d u) h (y) for all unitaries u ∈ A, all y ∈ A, and all d ∈ Z . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Hyers-Ulam-Rassias stability of an additive functional equation in quasi-Banach spaces

In this paper we investigate the Hyers-Ulam-Rassias stability of the following functional equation:

     

On the existence and stability for noninstantaneous impulsive fractional integrodifferential equation

In this paper, by means of Banach fixed point theorem, we investigate the existence and Ulam–Hyers–Rassias stability of the noninstantaneous impulsive integrodifferential equation by means of ψ‐Hilfer fractional derivative. In this sense, some examples are presented, in order to consolidate the results obtained.     

On the stability of a mixed functional equation deriving from additive,quadratic and cubic mappings

In this paper, we investigate the general solution and the Hyers–Ulam stability of the following mixed functional equation f(2x + y) + f(2x- y) = 2f(2x) + 2f(x + y) + 2f(x- y)- 4f(x)- f(y)- f(-y)deriving from additive, quadratic and cubic mappings on Banach spaces.     

Stability for quadratic functional equation in the spaces of generalized functions

In this paper, we consider the general solution of quadratic functional equation

f(ax+y)+f(ax−y)=f(x+y)+f(x−y)+2(a²−1)f(x)     

Stability of a quadratic Jensen type functional equation in the spaces of generalized functions

Making use of the fundamental solution of the heat equation we find the solution and prove the stability theorem of the quadratic Jensen type functional equation

     

Hyers–Ulam–Rassias Stability of a Jensen Type Functional Equation

In this paper we solve the Jensen type functional equation (1.1). Likewise, we investigate the Hyers–Ulam–Rassias stability of this equation.