Stability of an alternative functional equation related to Jensen's functional equation

Stability of an alternative Jensen’s functional equation

We prove the Hyers-Ulam stability of an alternative Jensen’s functional equation (f(x)+f(y))/2 = ±f((x+ y)/2) in the class of mappings from 2-divisible abelian groups to Banach spaces.

Hyers-Ulam Stability of Fibonacci Functional Equation

stability of the quadratic functional equation

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

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.

2-Banach stability results for the radical cubic functional equation related to quadratic mapping

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation$$fleft(sqrt[3]{ax^{3}+by^{3}}right)+fleft(sqrt[3]{ax^{3}-by^{3}}right)=2a^{2}f(x)+2b^{2}f(y),;; x,yinmathbb{R},$$for a mapping $f$ from $mathbb{R}$ into a vector space. We also investigate some stability and hyperstability results for...