In this paper, we will consider Hyers–Ulam–Rassias stability of multipliers and ring derivations between Banach algebras. As a corollary, we will prove superstability of ring derivations and multipliers. That is, approximate multipliers and approximate ring derivations are exact multipliers and ring derivations.

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation f(2x+ y) + f(2x− y) = 4(f(x+ y) + f(x− y))− 3 7 (f(2y)− 2f(y)) + 2f(2x) − 8f(x).

In this paper, we obtain the general solution and investigate the Hyers-Ulam-Rassias stability of the functional equation f(ax− y)± af(x± y) = (a± 1)[af(x)± f(y)] in non-Archimedean -fuzzy normed spaces. Mathematics Subject Classification: 39B55, 39B52, 39B82

Sometime in modeling applied problems there may be a degree of uncertainty in the parameters used in the model or some measurements may be imprecise. Due to such features, we are tempted to consider the study of functional equations in the fuzzy setting. The notion of fuzzy sets was first introduced by Zadeh [31] in 1965 which is a powerful hand set for modeling uncertainty and vagueness in var...

The existence aspects along with the stability of solutions to a Hadamard variable order fractional boundary value problem are investigated in this research study. Our results obtained via generalized intervals and piecewise constant functions relevant Green function, by converting existing an equivalent standard order. Further, Darbo’s fixed point criterion Kuratowski’s measure noncompactness ...

In this paper, the existence, uniqueness and stability of solutions to a boundary value problem nonlinear FDEs variable order are established. To do this, we first investigate some aspects operators Hadamard type. Then, with help generalized intervals piecewise constant functions, convert FBVP an equivalent standard BVP fractional order. Further, two fixed point theorems due Schauder Banach use...

The Langevin system is an important mathematical model to describe Brownian motion. research shows that fractional differential equations have more advantages in viscoelasticity. exploration of dynamics novel and valuable. Compared with the Caputo or Riemann–Liouville (RL) derivatives, Mittag–Leffler (ML)-type derivatives can eliminate singularity such solution has better analytical properties....

One of the interesting questions in the theory of functional equations concerning the problem of the stability of functional equations is as follows: when is it true that a mapping satisfying a functional equation approximately must be close to an exact solution of the given functional equation? The first stability problem was raised by Ulam during his talk at the University of Wisconsin in 194...

We apply the Luxemburg–Jung fixed point theorem in generalized metric spaces to study the Hyers–Ulam stability for two functional equations in a single variable.