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

We solve the inhomogeneous differential equation of the form y 2xy − 2ny ∞ m0 a m x m , where n is a nonnegative integer, and apply this result to the proof of a local Hyers-Ulam stability of the differential equation y 2xy − 2ny 0 in a special class of analytic functions.

In this paper, we define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation: f (x 1 + · · · + x l) = (l – 1)f x 1 + · · · + x l–1 l – 1 + f (x l) for a fixed integer l with l > 1, and prove the Hyers-Ulam stability of the generalized additive set-valued functional equation.

Using the fixed point method, we establish a generalized Ulam Hyers stability result for the monomial functional equation in the setting of complete random p-normed spaces. As a particular case, we obtain a new stability theorem for monomial functional equations in β-normed spaces.

An elastic beam equation (EBEq) described by a fourth-order fractional difference is proposed in this work with three-point boundary conditions involving the Riemann–Liouville operator. New sufficient ensuring solutions’ existence and uniqueness of problem are established. The findings obtained employing properties discrete equations, Banach contraction, Brouwer fixed-point theorems. Further, w...

Abstract In this study, an initial-value problem for a nonlinear Volterra functional integro-differential equation on finite interval was considered. The term in the contains multiple time delays. addition to giving some new theorems existence and uniqueness of solutions equation, authors also prove Hyers-Ulam-Rassias stability Hyers-Ulam equation. proofs use several different tools including B...

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...

In this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-Ulam stability. The arbitrary order is suggested in the sense of Riemann-Liouville calculus.

The Hyers–Ulam stability of the conditional quadratic functional equation of Pexider type f(x + y) + f(x − y) = 2g(x) + 2h(y), x ⊥ y is established where ⊥ is a symmetric orthogonality in the sense of Rätz and f is odd. ∗2000 Mathematics Subject Classification. Primary 39B52, secondary 39B82.

The generalized Hyers-Ulam-Rassias stability proposition in respect of the quadratic functional equation namely f(x+y+z)+f(x−y)+f(x−z) = f(x−y−z)+f(x+y)+f(x+z) is what is taken into account to be dealt with in this paper.