On the generalized Hyers–Ulam stability of multi-quadratic mappings

Generalized Stability of C∗-Ternary Quadratic Mappings

On the stability of multi-m-Jensen mappings

In this article, we introduce the multi-$m$-Jensen mappings and characterize them as a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability for such mappings. As a consequence, we show that every multi-$m$-Jensen mappings (under some conditions) is hyperstable.

Stability of Approximate Quadratic Mappings

In 1940, Ulam 1 gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems. Among these was the following question concerning the stability of homomorphisms. Let G1 be a group and let G2 be a metric group with metric ρ ·, · . Given > 0, does there exist a δ > 0 such that if f : G1 → G2 satisfies ρ f xy , f x f y < δ for all x, y ∈ ...

Stability of Mappings on Multi-normed Spaces

In this paper, we define multi-normed spaces, and investigate some properties of multi-bounded mappings on multi-normed spaces. Moreover, we prove a generalized Hyers– Ulam–Rassias stability theorem associated to the Cauchy additive equation for mappings from linear spaces into multi-normed spaces.

On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces

1 Youngs Researchers Club and Department of Basic Sciences, Islamic Azad University, Ayatollah Amoli Branch, P.O. Box 678, Amol, Iran 2 Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea 3 Department of Mechanical Engineering, Islamic Azad University, Ayatollah Amoli Branch, P.O. Box 678, Amol, Iran 4 Department of Mathematics and Compu...