Additive Functional Equation Research Articles

ADDITIVE FUNCTIONAL EQUATION WITH SEVERAL VARIABLES AND ITS STABILITY

In this paper, we prove the generalized Hyers{Ulam stability of an n-dimensional additive functional equation, and then apply stability results to Banach modules over a unital Banach algebras.

Stability of a Quartic and Additive Functional Equation in a 2-Banach Space

In this paper, we investigate the generalized Hyers-Ulam stability of the functional equation f(2x+y)+f(2x-y) = 4(f(x+y)+f(x-y))-3/7 (f(2y)-2f(y))+2f(2x)-8f(x) in 2-Banach space.

Homomorphisms and derivations on C∗-ternary algebras associated with a generalized Cauchy-Jensen type additive functional equation

In this paper, we prove the generalized Hyers-Ulam stability of C∗-ternary homomorphisms and C∗-ternary derivations on C∗-ternary algebras associated with the generalized Cauchy-Jensen type additive functional equationfor all xi; xj ∈ X where n ∈ Z+ is a fixed integer with n ≥ 3.ABSTRACTIn this paper, we prove the generalized Hyers-Ulam stability of ∁*-ternary homomorphisms and ∁*-ternary derivations on∁*-ternary algebras associated with the generalized Cauchy-Jensen type additive functional equation for all where  is a fixed integer with

Non-Archimedean and random HUR-approximation of a Cauchy-Jensen additive mapping

Abstract In this paper, using the fixed point and direct methods, we prove the Hyers-Ulam-Rassias approximation (briefly, HUR-approximation) of a Cauchy-Jensen additive (briefly, CJA) functional equation in various normed spaces. MSC:39B52, 39B82, 47H10, 46S10.

The fixed point alternative and Hyers-Ulam stability of generalized additive set-valued functional equations

We define generalized additive set-valued functional equations, which are related with the following generalized additive functional equations: f( x 1 +⋯+ x l )=(l−1)f( x 1 + ⋯ + x l − 1 l − 1 )+f( x l ), f ( x 1 + ⋯ + x l − 1 l − 1 + x l ) + f ( x 1 + ⋯ + x l − 2 + x l l − 1 + x l − 1 ) + ⋯ + f ( x 2 + ⋯ + x l l − 1 + x 1 ) = 2 [ f ( x 1 ) + f ( x 2 ) + ⋯ + f ( x l ) ] for a fixed integer l with l>1, and they prove the Hyers-Ulam stability of the generalized additive set-valued functional equations by using the fixed point method.MSC: 39B52, 54C60, 91B44.

On the stability of some functional equations in Menger φ-normed spaces

Abstract Recently, the authors [MIHEŢ, D.—SAADATI, R.—VAEZPOUR, S. M.: The stability of an additive functional equation in Menger probabilistic φ-normed spaces, Math. Slovaca 61 (2011), 817–826] considered the stability of an additive functional in Menger φ-normed spaces. In this paper, we establish some stability results concerning the cubic, quadratic and quartic functional equations in complete Menger φ-normed spaces via fixed point theory.

Stability of Functional Equations in Matrix Random Normed Spaces: A Fixed Point Approach

In this paper, we prove the Hyers–Ulam stability of the Cauchy additive functional equation and the quadratic functional equation in matrix random normed spaces by using fixed point method.

Approximate $$(\alpha ,\beta ,\gamma )$$ ( α , β , γ ) -derivation on random Lie $$C^*$$ C ∗ -algebras

In this paper, we define random Lie $$C^*$$ -algebras, then we apply a fixed point theorem to investigate some new stability results for $$(\alpha ,\beta ,\gamma )$$ -derivations on random Lie $$C^*$$ -algebras associated with a generalized Cauchy–Jensen type additive functional equation.

Hyers-Ulam-Rassias Stability of Some Additive Fuzzy Set-Valued Functional Equations with the Fixed Point Alternative

LetYbe a real separable Banach space and let𝒦CY,d∞be the subspace of all normal fuzzy convex and upper semicontinuous fuzzy sets ofYequipped with the supremum metricd∞. In this paper, we introduce several types of additive fuzzy set-valued functional equations in𝒦CY,d∞. Using the fixed point technique, we discuss the Hyers-Ulam-Rassias stability of three types additive fuzzy set-valued functional equations, that is, the generalized Cauchy type, the Jensen type, and the Cauchy-Jensen type additive fuzzy set-valued functional equations. Our results can be regarded as important extensions of stability results corresponding to single-valued functional equations and set-valued functional equations, respectively.

Stability of the n-dimensional mixed type additive and quadratic functional equation

Stability of the n-dimensional mixed type additive and quadratic functional equation

Stability of a mixed type additive and quartic functional equation

In this paper we obtain the general solution of a mixed additive and quartic functional equation. We also prove the Hyers-Ulam stability of this functional equation in random normed spaces.

On the Generalized Hyers-Ulam Stability of ann-Dimensional Quadratic and Additive Type Functional Equation

We investigate the generalized Hyers-Ulam stability of a functional equationf∑j=1n‍xj+(n-2)∑j=1n‍f(xj)-∑1≤i<j≤nf(xi+xj)=0.

Stability of a quadratic and additive type functional equation in random normed spaces

Stability of a quadratic and additive type functional equation in random normed spaces

On the non-Archimedean and random approximately general additive mappings: Direct and fixed point methods

In this paper, we prove the Hyers-Ulam stability of the following generalized additive functional equation ?1? i < j ? m f(xi+xj/2 + m-2?l=1,kl?i,j) = (m-1)2/2 m?i=1 f(xi) where m is a positive integer greater than 3, in various normed spaces.

On an n-dimensional mixed type additive and quadratic functional equation

In this paper, we investigate the generalized Hyers–Ulam stability of the functional equation∑k2,…,kn=01fx1+∑i=2n(-1)kixi-2n-1f(x1)-2n-2∑i=2nf(xi)+f(-xi)=0for integer values of n such that n⩾2, where f is a function from a normed space X to a Banach space Y. The solutions of the equation are called additive–quadratic mappings.

GENERALIZED HYERS-ULAM-RASSIAS STABILITY FOR A GENERAL ADDITIVE FUNCTIONAL EQUATION IN QUASI-β-NORMED SPACES

In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation , in quasi--normed spaces.

Functional equations and inequalities in matrix paranormed spaces

Abstract In this paper, we prove the Hyers-Ulam stability of the Cauchy additive functional inequality, the Cauchy additive functional equation and the quadratic functional equation in matrix paranormed spaces. MSC:47L25, 39B82, 39B72, 46L07, 39B52, 39B62.

Generalized Hyers-Ulam stability of derivations on Lie * C -algebras

In this paper, we investigate new generalized Hyers-Ulam stability results for (®; ¯; °)- derivations on Lie C¤-algebras associated with the following (m; n)-Cauchy-Jensen additive functional equation:

Approximation of homomorphisms and derivations on Lie "Equation missing" -algebras via fixed point method

Abstract In this paper, using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in C ∗ -algebras and Lie C ∗ -algebras and of derivations on C∗-algebras and Lie C∗-algebras for an m-variable additive functional equation. MSC:39A10, 39B52, 39B72, 46L05, 47H10, 46B03.

Fixed points and approximately heptic mappings in non-Archimedean normed spaces

Abstract Using the fixed point method, we investigate the stability of the system of additive, quadratic and quartic functional equations with constant coefficients in non-Archimedean normed spaces. Also, we give an example to show that some results in the stability of functional equations in (Archimedean) normed spaces are not valid in non-Archimedean normed spaces. MSC:39B82, 46S10, 47H10.