A fixed point theorem in n-Banach spaces and Ulam stability

On Ulam Stability of a Functional Equation

“…In this note, the Ulam stability of equation 4is shown. Moreover, we apply our main results (Theorems 2 and 7) to get some stability outcomes on functional equations (5) and 7.…”

Approximation of an Additive ϱ1,ϱ2-Random Operator Inequality

“…In [16,17], the authors studied the stability problem for fractional equations. Next, Cȃdariu et al [18][19][20] applied the fixed point method to solve the stability problem, and their work was continued by Keltouma et al [21], Park et al [22,23], Jung and Lee [24], and Brzdȩk and Ciepliński [25], see also [26,27].…”

“…Let (V, ξ, κ M ) be an MN-space, ρ < 1 and τ > 0. Suppose that T: Ω × U ⟶ V be a random operator satisfying T(ω, 0) � 0 and (25). erefore, there is a unique additive random operator S:…”

Approximate solution of generalized inhomogeneous radical quadratic functional equations in 2-Banach spaces

“…Recently, Brzdȩk and Ciepliński [11] proved a new fixed point theorem in 2-Banach spaces and showed its applications to the Ulam stability of some single-variable equations and the most important functional equation in several variables, namely, the Cauchy equation. And they extended the fixed point result to the n-normed spaces in [10]. Let us introduce the following hypotheses:…”