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

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 ...

Asymptotic behavior of alternative Jensen and Jensen type functional equations

In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982–2005 we established the Hyers–Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1998 S.-M. Jung and in 2002–2005 the authors of this paper investigated the Hyers–Ulam stability of additive ...

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.

On a new type of stability of a radical cubic functional equation related to Jensen mapping

‎The aim of this paper is to introduce and solve the‎ radical cubic functional equation‎ ‎$‎‎fleft(sqrt[3]{x^{3}+y^{3}}right)+fleft(sqrt[3]{x^{3}-y^{3}}right)=2f(x)‎$.‎ ‎We also investigate some stability and hyperstability results for‎ ‎the considered equation in 2-Banach spaces‎.