Functional inequalities for generalized multi-quadratic mappings

In this article, we introduce some special several variables mappings which are quadratic in each variable and show that such mappings can be defined as a single equation that is the generalized multi-quadratic functional equation. We also apply a fixed point theorem to establish the Hyers–Ulam stability for the generalized multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to some known stability results.

Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach

In this article, by using a new form of multi-quadratic mapping, we define multi-m-Jensen-quadratic mappings and then unify the system of functional equations defining a multi-m-Jensen-quadratic mapping to a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability of multi-quadratic and multi-m-Jensen-quadratic functional equations. As a consequence, we show that every multi-m-Jensen-quadratic functional equation (under some conditions) can be hyperstable.

Ulam Type Stability of ?-Quadratic Mappings in Fuzzy Modular ∗-Algebras

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.

Ulam Stability of a Functional Equation in Various Normed Spaces

In this note, we study the Ulam stability of a general functional equation in four variables. Since its particular case is a known equation characterizing the so-called bi-quadratic mappings (i.e., mappings which are quadratic in each of their both arguments), we get in consequence its stability, too. We deal with the stability of the considered functional equations not only in classical Banach spaces, but also in 2-Banach and complete non-Archimedean normed spaces. To obtain our outcomes, the direct method is applied.