On the Stability of Functional Equations and a Problem of Ulam

By Themistocles M. Rassias. 2000

701 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/51c31bd28fb14d0b5644ce85b5d30f8cc046f4f8

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Homomorphisms between Poisson JC*-Algebras (2005, background): “Several authors have investigated functional equations (see [1], [13]–[17]).”
A result of Tosio Aoki about a generalization of Hyers–Ulam stability of additive functions – a question of priority (2008, background): “Rassias [31], [32] and in 2003 by Soon-Mo Jung [25], but there is nothing there about the Aoki result from 1950.”
Isomorphisms between C*-ternary algebras (2006, neutral): “Rassias [26–29], F.”
STABILITY OF A FUNCTIONAL EQUATION DERIVING FROM QUARTIC AND ADDITIVE FUNCTIONS (2008, background): “This new concept is known as Hyers-Ulam-Rassias stability of functional equations (see [1,2], [5-11], [18-20]).”
Fixed Point Theory and the Ulam Stability (2014, background): “After his result a great number of papers (see for instance monographs [3–5], survey articles [6–14], and the references given there) on the subject have been published, generalizing Ulam’s problem and Hyers’s theorem in various directions and to other (not necessarily functional) equations.”
A fixed point approach to the stability of the cubic functional equation (2006, background): “For more detailed definitions of such terminologies, we can refer to [4], [6], [7], [9], [10], [14].”
Discrete Spectral Synthesis and Its Applications (2006, background): “The volumes [28] and [29] and the research papers [27] and [48] present the newest methods of stability theory of functional equations, while [47] and [9] offer a more detailed collection of recent results on functional equations in several variables.”
Hyers–Ulam stability of delay differential equations of first order (2016, background): “[3], [9], [20], [34], [36]–[38], many mathematicians paid attention to the problem of differential equations, for the papers concerning ordinary differential equations we refer the readers to [10], [15], [21], [23]–[25], [28], [30], [32], [41].”
Hyers-Ulam-Rassias Stability for a First Order Functional Differential Equation (2015, methodology): “Since then, the stability problems of various functional equations have been investigated by many authors (see [1-17]).”