Additive-quadratic Functional Equation Research Articles

On an alternative additive-quadratic functional equation

On an alternative additive-quadratic functional equation

Generalized Hyers-Ulam stability of a 3D additive-quadratic functional equation in Banach spaces: A study with counterexamples

In this research, we focus on solving a mixed type additive-quadratic functional equation expressed as:\begin{align*}h(3s_1+2s_2+s_3) + h(3s_1+2s_2-s_3) + h(3s_1-2s_2+s_3)+&h(3s_1-2s_2-s_3)\\= &12\tilde{h}(s_1) +8\tilde{h}(s_2)+2\tilde{h}(s_3)+12h(s_1)\end{align*}where $\tilde{h}(s_1)=h(s_1)+h(-s_1)$ is derived. We proceed to investigate the generalized Hyers-Ulam stability of this equation within the framework of Banach spaces, employing the Hyers direct method. Additionally, examples of non-stable cases are also provided.

General Solution and Stability of Additive-Quadratic Functional Equation in IRN-Space

The investigation of the stabilities of various types of equations is an interesting and evolving research area in the field of mathematical analysis. Recently, there are many research papers published on this topic, especially additive, quadratic, cubic, and mixed type functional equations. We propose a new functional equation in this study which is quite different from the functional equations already dealt in the literature. The main feature of the equation dealt in this study is that it has three different solutions, namely, additive, quadratic, and mixed type functions. We also prove that the stability results hold good for this equation in intuitionistic random normed space (briefly, IRN-space).

An additive-quadratic functional equation in intuitionistic fuzzy normed spaces

In this work, we investigate the stability of additive-quadratic (AQ) functional equation in intuitionistic fuzzy normed spaces

Hyers-Ulam stability of an additive-quadratic functional equation

In this paper, we introduce the following \((a,b,c)\)-mixed type functional equation of the form \(g(ax_1+bx_2+cx_3 )-g(-ax_1+bx_2+cx_3 ) + g(ax_1-bx_2+cx_3 )\)\(-g(ax_1+bx_2-cx_3 ) + 2a^2 [g(x_1 ) + g(-x_1)] + 2b^2 [g(x_2 ) + g(-x_2)] + \)\(2c^2 [g(x_3 ) + g(-x_3)]+a[g(x_1 ) - g(-x_1)]+ b[g(x_2 )-g(-x_2)] + \) \(c[g(x_3 )-g(-x_3)]=4g(ax_1+cx_3 )+2g(-bx_2)+\) \(2g(bx_2)\) where \(a,b,c\) are positive integers with \(a>1\), and investigate the solution and the Hyers-Ulam stability of the above functional equation in Banach spaces by using two different methods.

A Characterization of Multi-Mixed Additive-Quadratic Mappings and a Fixed Point Application

In this paper, we introduce $$n$$ -variables mappings which are mixed additive-quadratic in each variable. We show that such mappings can be described by a equation, namely, by a multi-mixed additive-quadratic functional equation. The main goal is to extend the applications of a fixed point method to establish the Hyers-Ulam stability for the multi-mixed additive-quadratic mappings.

Ulam stability of an additive-quadratic functional equation in Banach spaces

Ulam stability of an additive-quadratic functional equation in Banach spaces

Stability of an <i>n</i>-variable mixed type functional equation in probabilistic modular spaces

In this research paper, we solve a new n-variable mixed type additive-quadratic functional equation and prove the Ulam stability of the new n-variable mixed type additive-quadratic functional equation in probabilistic modular spaces by using fixed point method.

Generalized Hyers-Ulam Stability Of Mixed Type Additive-Quadratic Functional Equation Of Random Homomorphisms In Random Normed Algebras

In this paper, by the fixed point method, we prove the generalized stability of random homomorphisms of the following additive-quadratic functional equation f(2 + y) + f(2 − y) = 2[f(x + y) + f(x − y)] + 2[f(x) + f(−x)] − [f(y) + f(−y)], in random normed algebras.

On Approximation Solutions of the Cauchy-Jensen and the Additive-Quadratic Functional Equation in Paranormed Spaces

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the bi-Cauchy-Jensen functional equation and the bi-additive-quadratic functional equation in paranormed spaces. Moreover, we investigate the Hyers-Ulam-Rassias stability of the generalized Cauchy-Jensen equation in such spaces.

Ulam stability of a alternate additive-quadratic functional equation in IFB space

Ulam stability of a alternate additive-quadratic functional equation in IFB space

On The Oscillation of Impulsive Neutral Partial Differential Equations with Distributed Deviating Arguments and Damping Term

In this paper, we establish the Hyers-Ulam stability of the following Orthogonally Additive-Quadratic functional equation in Multi-Banach Spaces.ζ(2i + j) − ζ(i + 2j) − ζ(i + j) − ζ(j − i) − ζ(i) + ζ(j) + ζ(2j) = 0 with i⊥j where, ⊥ is orthogonality in the sense of Ratz.

Stability of Orthogonally Additive-Quadratic Functional Equation in Multi-Banach Spaces

Stability of Orthogonally Additive-Quadratic Functional Equation in Multi-Banach Spaces

English

English

Solution and fuzzy stability of a mixed type functional equation

AbstractIn this paper, we obtain the general solution and we study the generalized Hyers–Ulam stability of the mixed type additive-quadratic functional equation

Intuitionistic random almost additive-quadratic mappings

Abstract In this paper, we investigate the Hyers-Ulam stability of the additive-quadratic functional equation ∑ i = 1 n f ( x i − 1 n ∑ j = 1 n x j ) = ∑ i = 1 n f ( x i ) − n f ( 1 n ∑ i = 1 n x i ) ( n ≥ 2 ) in intuitionistic random normed spaces. MSC:39B52, 34K36, 46S50, 47S50, 34Fxx.

Hyers-Ulam-Rassias stability of the additive-quadratic mappings in non-Archimedean Banach spaces

Abstract Using the fixed point and direct methods, we prove the generalized Hyers-Ulam stability of the following additive-quadratic functional equation in non-Archimedean normed spaces r [ f ( x + y + z s ) + f ( x − y + z s ) + f ( x + y − z s ) + f ( − x + y + z s ) ] = γ f ( x ) + γ f ( y ) + γ f ( z ) , where r, s, γ are positive real numbers. MSC:39B55, 46S10.

Fuzzy Hyers-Ulam approximation of a mixed AQ mapping

Abstract In this article, we adopt the fixed point and direct methods to prove the Hyers-Ulam stability for an additive-quadratic functional equation in fuzzy Banach spaces. Mathematics Subject Classification 2010: 39B52, 46S40; 26E50.

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.

Orthogonal Stability of an Additive-Quadratic Functional Equation

AbstractUsing the fixed point method and using the direct method, we prove the Hyers-Ulam stability of an orthogonally additive-quadratic functional equation in orthogonality spaces.(2010) Mathematics Subject Classification: Primary 39B55; 47H10; 39B52; 46H25.