Solution and Stability of a Mixed Type Cubic and Quartic Functional Equation in Quasi-Banach Spaces
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In this article, the generalized Ulam-Hyer stability of the mixed type cubic and quartic functional equation in quasi-Banach spaces was obtained. But the general solution was not given.Abstract:Β
We obtain the general solution and the generalized Ulam-Hyers stability of the mixed type cubic and quartic functional equation in quasi-Banach spaces.read more
Citations
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Nearly Ring Homomorphisms and Nearly Ring Derivations on Non-Archimedean Banach Algebras
TL;DR: In this paper, the generalized Hyers-Ulam stability of homomorphisms and derivations on non-archimedean Banach algebras was shown to be robust.
Journal ArticleDOI
Stability of mixed additive-quadratic Jensen type functional equation in various spaces
Hassan Azadi Kenary,Yeol Je Cho +1 more
TL;DR: The generalized Hyers-Ulam stability of the following mixed additive-quadratic functional equation 2f(x+y2)+f (x-y2)-f (y-x2)+ f(x)+f(y) in various spaces is proved.
Journal ArticleDOI
On nonlinear stability in various random normed spaces
TL;DR: In this paper, the authors prove the nonlinear stability of the quartic functional equation in the setting of random normed spaces and the interdisciplinary relation among the theory of random spaces and functional equations.
Journal ArticleDOI
The Fixed Point Method for Fuzzy Approximation of a Functional Equation Associated with Inner Product Spaces
M. Eshaghi Gordji,Hamid Khodaei +1 more
TL;DR: In this paper, the authors extend the fixed point alternative method to provide a fuzzy stability for the functional equation βππ=1π(π₯ Η«ββ(1/Η«)Η« βΗ«(Η« )βΗ« (Η«)-Η« β 0.
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Generalized Ulam-Hyers Stability of Jensen Functional Equation in Ε erstnev PN Spaces
TL;DR: In this article, the Ulam-Hyer stability theorem in a Serstnev probabilistic normed space (briefly referred to as PN-space) was established.
References
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On the Stability of the Linear Functional Equation
TL;DR: This program includes in particular the complete theory of the convergence and divergence of formal series, the explicit determination of the essential transcendental invariants, the inverse Riemann theory both for the neighborhood of x = o and in the complete plane, explicit integral representation of the solutions, and finally the definition of q-sigma periodic matrices.
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On the stability of the linear mapping in Banach spaces
TL;DR: In this article, the authors give an answer to Ulam's problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist", and prove it for the case n = 1.
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A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings
TL;DR: In this paper, a generalization of the stability of additive mappings has been proposed in the spirit of Hyers, Ulam, and Rassias, and the stability has been shown to be robust.
Book
Stability of Functional Equations in Several Variables
TL;DR: Approximate additive and approximately linear mappings stability of the quadratic functional equation generalizations, the method of invariant means approximately multiplicative mappings, superstability stability of functional equations for trigonometric and similar functions functions functions with bounded nth differences, stability of generalized orthogonality functional equation stability and set-valued mappings Stability of stationary and minimum points functional congruences quasi-additive functions and related topics as mentioned in this paper.