In this paper, we study the Hyers-Ulam-Rassias stability of the quadratic functional equation f(x + y) + f(x − y) = 2f(x) + 2f(y), x⊥y in which ⊥ is orthogonality in the sens of Rätz in modular spaces.

In this paper, some nonlinear Gronwall–Bellman type inequalities are established. Then, the obtained results are applied to study the Hyers–Ulam stability of a fractional differential equation and the boundedness of solutions to an integral equation, respectively.

In this paper we prove result for Jensen type mapping in the setting of intuitionistic fuzzy normed spaces. We generalize a Hyers-Ulam stability result in the framework of classical normed spaces.

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.

We study the approximate solution of special type \(n^{th}\) order linear differential equation by applying initial and boundary conditions using Taylor's series formula. That is, we prove sufficient condition for Mittag-Leffler-Hyers-Ulam stability Mittag-Leffler-Hyers-Ulam-Rassias higher with

In this paper, we establish the generalized Hyers–Ulam–Rassias stability of homomorphisms between ternary algebras associted to the generalized Jensen functional equation rf( sx+ty r ) = sf(x) + tf(y).

In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C-ternary ring homomorphisms associted to the Trif functional equation d · C d−2f( x1 + · · ·+ xd d ) + C d−2 d ∑

The Hyers–Ulam–Rassias stability of the conditional quadratic functional equation of Pexider type f (x+y)+f (x−y) = 2g(x)+2h(y), x ⊥ y is proved where ⊥ is the orthogonality in the sense of Rätz.

In this paper, the solution and the Hyers–Ulam stability of the following quadratic type functional equation k ∑ i=2 ∑ "j∈{−1,1} f (x1 + "jxi) = 2(k − 1)f(x1) + 2 k ∑

In this paper we obtain a result on Hyers-Ulam stability of the linear functional equation in a single variable f(φ(x)) = g(x) · f(x) on a complete metric group.