Abstract
In this paper, we find the solution of the following quadratic functional equation n∑1≤i<j≤nQxi−xj=∑i=1nQ∑j≠ixj−(n−1)xi, which is derived from the gravity of the n distinct vectors x1,⋯,xn in an inner product space, and prove that the stability results of the A-quadratic mappings in μ-complete convex fuzzy modular ∗-algebras without using lower semicontinuity and β-homogeneous property.
Highlights
A concept of stability in the case of homomorphisms between groups was formulated by S.M.Ulam [1] in 1940 in a talk at the University of Wisconsin
In this paper, we find the solution of the following quadratic functional equation n n ∑1≤i< j≤n Q xi − x j = ∑i=1 Q ∑ j6=i x j − (n − 1) xi, which is derived from the gravity of the n distinct vectors x1, · · ·, xn in an inner product space, and prove that the stability results of the A-quadratic mappings in μ-complete convex fuzzy modular ∗-algebras without using lower semicontinuity and β-homogeneous property
J 6 =i which is derived from the gravity of the n-distinct vectors in an inner product space, we investigate the stability problem for A-quadratic mappings in μ-complete convex fuzzy modular ∗-algebras of the following functional equation without using lower semicontinuity and β-homogeneous property
Summary
A concept of stability in the case of homomorphisms between groups was formulated by S.M. The first affirmative answer to the question of Ulam was given by Hyers [2,3] for the Cauchy functional equation in Banach spaces as follows: Let X and Y be Banach spaces. Using Khamsi’s fixed point theorem in modular spaces [17], Wongkum and Kumam [18] proved the stability of sextic functional equations in fuzzy modular spaces equipped necessarily with lower semicontinuity and β-homogeneous property. In a recent paper [11], Ulam stability of the following additive functional equation. In the present paper, concerning the stability problem for the following functional equation n n. J 6 =i which is derived from the gravity of the n-distinct vectors in an inner product space, we investigate the stability problem for A-quadratic mappings in μ-complete convex fuzzy modular ∗-algebras of the following functional equation without using lower semicontinuity and β-homogeneous property
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