We present a novel generalization of the Hyers–Ulam–Rassias stability definition to study generalized cubic set-valued mapping in normed spaces. In order achieve our goals, we have applied brand new fixed point alternative. Meanwhile, obtained practicable example demonstrating that is not defined as stable according previously methods and procedures.

1. A. H. Sales, About K-Fibonacci numbers and their associated numbers; Int. J. of Math Forum, Vol. 6, no.50, (2011) 24732479. 2. D. H. Hyers, On the stability if linear functional equation, Proc. Natl. Acad. Sci. USA. 27(1941) 221-224. 3. D. H. Hyers, G. Isac and Th. M Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Boston, 1998. 4. D. H. Hyers and Th. M. Rassias, ...

We study the existence and uniqueness of solutions for coupled Langevin differential equations fractional order with multipoint boundary conditions involving generalized Liouville–Caputo derivatives. Furthermore, we discuss Ulam–Hyers stability in context problem at hand. The results are shown examples. Results asymmetric when a derivative (ρ) parameter is changed.

The study of stability problems of functional equations was motivated by a question of S.M. Ulam asked in 1940. The first result giving answer to this question is due to D.H. Hyers. Subsequently, his result was extended and generalized in several ways.We prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=Ag(x)+Bg(y)on restricted domain. Namely, we show, under some weak natural...

In this paper, we investigate the generalized Hyers-Ulam stability of Jordan homomorphisms in Jordan Banach algebras for the functional equation begin{align*} sum_{k=2}^n sum_{i_1=2}^ksum_{i_2=i_{1}+1}^{k+1}cdotssum_{i_n-k+1=i_{n-k}+1}^n fleft(sum_{i=1,i not=i_{1},cdots ,i_{n-k+1}}^n x_{i}-sum_{r=1}^{n-k+1} x_{i_{r}}right) + fleft(sum_{i=1}^{n}x_{i}right)-2^{n-1} f(x_{1}) =0, end{align*} where ...

In this paper, we investigate the exact and approximate controllability, finite time stability, β–Hyers–Ulam–Rassias stability of a fractional order neutral impulsive differential system. The controllability criteria is incorporated with help fixed point approach. famous generalized Grönwall inequality used to study stability. Finally, main results are verified an example.