Stability of Unbounded Differential Equations in Menger k-Normed Spaces: A Fixed Point Technique

Abstract

We attempt to solve differential equations υ ′ ( ν ) = Γ ( ν , υ ( ν ) ) and use the fixed point technique to prove its Hyers–Ulam–Rassias stability in Menger k-normed spaces.

Radu–Miheţ method for UHML stability for a class of ξ‐Hilfer fractional differential equations in matrix valued fuzzy Banach spaces

“…Approximation of functional equations was studied in MVFN spaces, fuzzy metric spaces and random multi‐normed space 7–10 . Also, stability results for stochastic fractional differential and integral equations were considered in previous works 11–18 …”

“…Approximation of functional equations was studied in MVFN spaces, fuzzy metric spaces and random multi-normed space. [7][8][9][10] Also, stability results for stochastic fractional differential and integral equations were considered in previous works. [11][12][13][14][15][16][17][18] Now, we present an alternative fixed point theorem from the literature:…”

Ulam–Hyers–Rassias stability for nonlinear Ψ-Hilfer stochastic fractional differential equation with uncertainty

“…The subject of approximation of functional equations in several spaces by direct techniques and fixed point techniques have been studied by some researchers, for instance, fuzzy Menger normed algebras [19], fuzzy metric spaces [20,21], FN spaces [22], non-Archimedean random Lie C * -algebras [23], and random multinormed space [24][25][26][27][28][29]. Some stability results for fractional differential and integral equations have been discussed in [26,[30][31][32][33][34][35][36][37][38].…”

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

“…In the same year, Alanazi et al [29] proved the fuzzy stability results of a finite variable additive functional equation using direct and fixed point methods. Madadi et al [30] published ground-breaking work on the stability of unbounded differential equations in Menger k-normed spaces using a fixed point technique. Liu et al [31] presented a fixed-point approach to the Hyers-Ulam stability (HUS) of Caputo-Fabrizio fractional differential equations.…”