A fixed point approach to the stability of a generalized Cauchy functional equation

A Fixed Point Approach to the Stability of a Generalized Cauchy Functional Equation

We investigate the following generalized Cauchy functional equation f(αx+ βy) = αf(x) + βf(y) where α, β ∈ R \ {0}, and use a fixed point method to prove its generalized Hyers–Ulam–Rassias stability in Banach modules over a C∗-algebra.

A Fixed Point Approach to the Stability of a Cauchy-Jensen Functional Equation

and Applied Analysis 3 Theorem 2.2. A mapping f : X ×X → Y satisfies 1.1 if and only if it satisfies 1.2 . Proof. If f satisfies 1.1 , then we get

A Fixed Point Approach to the Stability of the Cauchy Additive and Quadratic Type Functional Equation

A fixed point approach to the Hyers-Ulam stability of an $AQ$ functional equation in probabilistic modular spaces

In this paper, we prove the Hyers-Ulam stability in$beta$-homogeneous probabilistic modular spaces via fixed point method for the functional equation[f(x+ky)+f(x-ky)=f(x+y)+f(x-y)+frac{2(k+1)}{k}f(ky)-2(k+1)f(y)]for fixed integers $k$ with $kneq 0,pm1.$

A FIXED POINT APPROACH TO THE INTUITIONISTIC FUZZY STABILITY OF QUINTIC AND SEXTIC FUNCTIONAL EQUATIONS

The fixed point alternative methods are implemented to giveHyers-Ulam  stability for  the quintic functional equation $ f(x+3y)- 5f(x+2y) + 10 f(x+y)- 10f(x)+ 5f(x-y) - f(x-2y) = 120f(y)$ and thesextic functional equation $f(x+3y) - 6f(x+2y) + 15 f(x+y)- 20f(x)+15f(x-y) - 6f(x-2y)+f(x-3y) = 720f(y)$   in the setting ofintuitionistic fuzzy normed spaces (IFN-spaces).  This methodintroduces a met...