On the Ulam stability of Jensen and Jensen type mappings on restricted domains

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 a Generalized Jensen Equation on Restricted Domains

In this paper, we establish the conditional stability of the generalized Jensen functional equation f (ax+by) = ag(x)+bh(y) on various restricted domains such as inside balls, outside balls, and punctured spaces. In addition, we prove the orthogonal stability of this equation and study orthogonally generalized Jensen mappings on balls in inner product spaces.

Stability of Generalized Jensen Equation on Restricted Domains

In this paper, we establish the conditional Hyers-Ulam-Rassias stability of the generalized Jensen functional equation r f ( sx+ty r ) = s g(x) + t h(y) on various restricted domains such as inside balls, outside balls, and punctured spaces. In addition, we prove the orthogonal stability of this equation and study orthogonally generalized Jensen mappings on Balls in inner product spaces.

Stability of Jensen-Type Functional Equations on Restricted Domains in a Group and Their Asymptotic Behaviors

Stability of a Jensen Type Logarithmic Functional Equation on Restricted Domains and Its Asymptotic Behaviors

Let R be the set of positive real numbers, B a Banach space, f : R → B, and > 0, p, q, P,Q ∈ R with pqPQ/ 0. We prove the Hyers-Ulam stability of the Jensen type logarithmic functional inequality ‖f xy − Pf x − Qf y ‖ ≤ in restricted domains of the form { x, y : x > 0, y > 0, xy ≥ d} for fixed k, s ∈ R with k / 0 or s / 0 and d > 0. As consequences of the results we obtain asymptotic behaviors ...