Type Additive Functional Equation Research Articles

Stability Analysis of a New Class of Series Type Additive Functional Equation in Banach Spaces: Direct and Fixed Point Techniques

In this paper, the authors introduce two new classes of series type additive functional Equations (FEs). The first class of equations is derived from the sum of the squares of the alternative series and the second one is obtained from the sum of the cubes of the series. The solution of the FE is investigated using the principle of mathematical induction. The beauty of this method lies in the fact that it satisfies the property of the additive FE as well as the series. Banach spaces are one of the widely-used spaces that are very helpful to analyse the stability results of various FEs. The Banach space conditions have been applied and the stability results are established for both of the equations. Furthermore, the Banach Contraction principle and alternative of fixed point theorem are used to derive the stability results in a fixed point technique (FPT). The relationship between the FEs and both the series is established through the principle of mathematical induction in the Application section, which adds novelty to the derived results.

Stability of a ramanujan type additive functional equation

In this paper, the authors achieve the generalized Ulam - Hyers stability of a Ramanujan Type Additive Functional Equation in Paranormed Spaces and Modular spaces via classical Hyers Method.

Ulam Stability of new type additive functional equation in Multi-Banach Spaces

In this Paper, we establish the General solution and stability of a new type additive functional equation is of the form f(2x + 5y) − f(x + 4y) = f(x) + f(y) in Multi-BanachSpace in the sense of Hyers-Ulam.

Stability of the Apollonius Type Additive Functional Equation in Modular Spaces and Fuzzy Banach Spaces

In this work, we investigate the generalized Hyers-Ulam stability of the Apollonius type additive functional equation in modular spaces with or without Δ 2 -conditions. We study the same problem in fuzzy Banach spaces and β -homogeneous Banach spaces. We show the hyperstability of the functional equation associated with the Jordan triple product in fuzzy Banach algebras. The obtained results can be applied to differential and integral equations with kernels of non-power types.

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

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.

C*-TERNARY HOMOMORPHISMS, C*-TERNARY DERIVATIONS, JB*-TRIPLE HOMOMORPHISMS AND JB*-TRIPLE DERIVATIONS

Park and Rassias proved the superstability of C*-ternary homomorphisms, C*-ternary derivations, JB*-triple homomorphisms and JB*-triple derivations, associated with the following Apollonius type additive functional equation [Formula: see text] by using direct method. Under the conditions of the theorems, we can show that the mappings f must be zero. In this paper, we correct the conditions. Furthermore, we prove the superstability of C*-ternary homomorphisms, C*-ternary derivations, JB*-triple homomorphisms and JB*-triple derivations by using fixed point method.

A fixed point technique for investigating the stability of [formula omitted]-derivations on Lie [formula omitted]-algebras

We apply a fixed point theorem to investigate some new stability results for (α,β,γ)-derivations on Lie C∗-algebras associated with the generalized Cauchy–Jensen type additive functional equation ∑i=1nf(xi+1n−1∑j=1,j≠inxj)=2∑i=1nf(xi).

Non-Archimedean Hyers-Ulam-Rassias stability of m-variable functional equation

Abstract The main goal of this paper is to study the Hyers-Ulam-Rassias stability of the following Euler-Lagrange type additive functional equation: ∑ j = 1 m f ( − r j x j + ∑ 1 ≤ i ≤ m , i ≠ j r i x i ) + 2 ∑ i = 1 m r i f ( x i ) = m f ( ∑ i = 1 m r i x i ) , where r 1 , … , r m ∈ R , ∑ i = k m r k ≠ 0 , and r i , r j ≠ 0 for some 1 ≤ i < j ≤ m , in non-Archimedean Banach spaces. MSC:39B22, 39B52, 46S10.

Stability of homomorphisms for a 3D Cauchy–Jensen type functional equation on [formula omitted]-ternary algebras

In this paper, we investigate homomorphisms between C ∗ -ternary algebras, and derivations on C ∗ -ternary algebras associated with the following Cauchy–Jensen type additive functional equation: f ( x + y 2 + z ) + f ( x + z 2 + y ) + f ( y + z 2 + x ) = 2 ( f ( x ) + f ( y ) + f ( z ) ) .