Quadratic-additive Functional Equation Research Articles

Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ-2-Normed Spaces and Non-Archimedean Banach Spaces

In this work, we introduce a new type of generalized mixed-type quadratic-additive functional equation and obtain its general solution. The main goal of this work is to investigate Ulam stability of this mixed type of quadratic-additive functional equation in the setting of non-Archimedean fuzzy φ-2-normed space and non-Archimedean Banach space using the direct and fixed point approaches by taking into our account two cases: even mapping and odd mapping.

Stability Results of Quadratic-Additive Functional Equation Based on Hyers Technique in Matrix Paranormed Spaces

In this work, we introduce a mixed type of quadratic-additive (QA) functional equation and obtain its general solution. The objective of this work is to investigate the Ulam–Hyers stability of this quadratic-additive (QA) functional equation in matrix paranormed spaces (briefly, MP spaces) using the Hyers method for the factor sum of norms.

Stability Results of Mixed Type Quadratic-Additive Functional Equation in β-Banach Modules by Using Fixed-Point Technique

We aim to introduce the quadratic-additive functional equation (shortly, QA-functional equation) and find its general solution. Then, we study the stability of the kind of Hyers-Ulam result with a view of the aforementioned functional equation by utilizing the technique based on a fixed point in the framework of β-Banach modules. We here discuss our results for odd and even mappings as well as discuss the stability of mixed cases.

Ulam stability of a functional equation deriving from quadratic and additive mappings in random normed spaces

The aim of this work is to introduce a new mixed type quadratic-additive functional equation, to obtain its general solution and to investigate Ulam stability by using Hyers method in random normed spaces.

Hyers-Ulam stability of a finite variable mixed type quadratic-additive functional equation in quasi-Banach spaces

In this paper, we introduce a mixed type finite variable functional equation deriving from quadratic and additive functions and obtain the general solution of the functional equation and investigate the Hyers-Ulam stability for the functional equation in quasi-Banach spaces.

A general theorem on the stability of a class of functional equations including quadratic-additive functional equations.

We prove a general stability theorem of an n-dimensional quadratic-additive type functional equation \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} Df(x_1, x_2, \\ldots , x_n) = \\sum _{i=1}^m c_i f \\big ( a_{i1}x_1 + a_{i2}x_2 + \\cdots + a_{in}x_n \\big ) = 0 \\end{aligned}$$\\end{document}Df(x1,x2,…,xn)=∑i=1mcif(ai1x1+ai2x2+⋯+ainxn)=0by applying the direct method.

Stability of a Jensen type quadratic-additive functional equation under the approximately conditions

We prove the Hyers-Ulam-Rassias stability of the Jensen type quadratic and additive functional equation \(9f ( \frac{x+y+z}{3} ) + 4 [ f (\frac{x-y}{2} ) + f (\frac{y-z}{2} ) + f (\frac{z-x}{2} ) ] = 3 [ f(x)+f(y)+f(z) ]\) under the approximately conditions such as even, odd, quadratic, and additive in Banach spaces.

On the Ulam stability of mixed type QA mappings in IFN-spaces

We give Ulam-type stability results concerning the quadratic-additive functional equation in intuitionistic fuzzy normed spaces.

On the stability of a mixed type quadratic-additive functional equation

In this paper we establish the general solutions of the following mixed type quadratic-additive functional equation: in the class of functions between real vector spaces. Moreover, we prove the generalized Hyers-Ulam-Rassias stability of this equation in Banach spaces. MSC:39B82, 39B52.