Perturbation of n dimensional AQ - mixed type functional equation via Banach spaces and Banach algebra : Hyers direct and alternative fixed point methods

Stability of a Mixed Type Functional Equation on Multi-Banach Spaces: A Fixed Point Approach

Approximate mixed additive and quadratic functional in 2-Banach spaces

In the paper we establish the general solution of the function equation f(2x+y)+f(2x-y) = f(x+y)+f(x-y)+2f(2x)-2f(x) and investigate the Hyers-Ulam-Rassias stability of this equation in 2-Banach spaces.

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 $kneq 0,pm1.$

On the Hyers-Ulam Stability of a General Mixed Additive and Cubic Functional Equation in n-Banach Spaces

and Applied Analysis 3 Definition 1.4. A sequence {xk} in an n-normed space X is said to converge to some x ∈ X in the n-norm if lim k→∞ ∥ ∥xk − x, y2, . . . , yn ∥ ∥ 0, 1.4 for every y2, . . . , yn ∈ X. Definition 1.5. A sequence {xk} in an n-normed space X is said to be a Cauchy sequence with respect to the n-norm if lim k,l→∞ ∥ ∥xk − xl, y2, . . . , yn ∥ ∥ 0, 1.5 for every y2, . . . , yn ∈ X...

Stability of the Jensen–type functional equation in ternary Banach algebras: An alternative fixed point approach

Using fixed point methods, we prove the generalized Hyers–Ulam–Rassias stability of ternary homomorphisms, and ternary multipliers in ternary Banach algebras for the Jensen–type functional equation f( x+ y + z 3 ) + f( x− 2y + z 3 ) + f( x+ y − 2z 3 ) = f(x) .