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Article
Open AccessLocal stability of map**s on multi-normed spaces
First we investigate the Hyers–Ulam stability of the Cauchy functional equation for map**s from bounded (unbounded) intervals into Banach spaces. Then we study the Hyers–Ulam stability of the functional equa...
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Article
Approximate homomorphisms from ternary semigroups to modular spaces
In this article, we investigate the generalized Hyers–Ulam stability of ternary homomorphisms from ternary semigroups into modular spaces. Ternary algebraic structures appear in theoretical and mathematical ph...
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Hyers–Ulam Stability of First Order Differential Equation via Integral Inequality
In this chapter, first we derive a nonlinear integral inequality of Gollwitzer type, and as an application we investigate the Hyers–Ulam stability of nonlinear differential equation y ′ ( t ) = f ( t , y ( t )
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Article
Open AccessStability and nonstability of octadecic functional equation in multi-normed spaces
In this paper, we introduce octadecic functional equation. Moreover, we prove the stability of the octadecic functional equation in multi-normed spaces by using the fixed point method.
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Article
Approximation of General 𝛼-Cubic Functional Equations in 2-Banach Spaces
We introduce a new α-cubic functional equation and investigate the generalized Hyers–Ulam stability of this functional equation in 2-Banach spaces.
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Article
Open AccessUlam stability of a generalized reciprocal type functional equation in non-Archimedean fields
In this paper, we obtain the solution of a new generalized reciprocal type functional equation in two variables and investigate its generalized Hyers–Ulam stability in non-Archimedean fields. We also present t...
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Article
Approximation of a General Cubic Functional Equation in Felbin’s Type Fuzzy Normed Linear Spaces
In this paper, we investigate the generalized Hyers–Ulam stability of a general cubic functional equation in Felbin’s type fuzzy normed linear spaces and some applications of our results in the stability of ge...
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Article
A generalized mixed type of quartic–cubic–quadratic–additive functional equations
We determine the general solution of the functional equation f(x + ky) + f(x-ky) = g(x + y) + g(x-y) + h(x) + h(y) for fixed integers with k ≠ 0; ±1 without assuming any regularity conditions for the unknown func...
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Article
Open AccessSuperstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I)
We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let be a Ba...
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Article
Open AccessSolution and Stability of a Mixed Type Additive, Quadratic, and Cubic Functional Equation
We obtain the general solution and the generalized Hyers-Ulam-Rassias stability of the mixed type additive, quadratic, and cubic functional equation ...
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Article
On the Hyers-Ulam stability problem for quadratic multi-dimensional map**s
In 1940 S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved this problem for linear map**s. According to P. M. Gruber (1978) this kind of stability problems is of particu...
