On the Stability of Functional Equations in Banach Spaces

By Themistocles M. Rassias. 2000

587 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/59bf70c3f99c4361e22ccd1f49df82dce6342b46

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

The Generalized Hyers--Ulam--Rassias Stability of a Cubic Functional Equation (2007, background): “For more detailed definitions of such terminologies, we refer the reader to [8, 10, 16].”
Stability of a Functional Equation Deriving from Cubic and Quartic Functions (2008, background): “This new concept is known as Hyers-Ulam-Rassias stability of functional equations (see [1-2], [5-10], [28-30]).”
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.”
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]).”
Isomorphisms between C*-ternary algebras (2006, unknown): “Rassias [26–29], F.”
On the stability of the linear mapping in Banach modules (2002, background): “The stability problems of functional equations have been investigated in several papers [5,8,9,11].”
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.”
Applications of fixed point theorems to the Hyers-Ulam stability of functional equations–a survey (2012, background): “After his result a great number of papers (see for instance monographs [23, 26, 29], survey articles [1, 18, 24, 39, 40, 43] 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 equations (as the words ”