Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis

By Soon-Mo Jung. 2011

687 citations recorded by the source corpus.

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In Applied Mathematics

Citations in the corpus

Hyers-Ulam stability of first-order non-linear delay differential equations with fractional integrable impulses (2017, background): “For further details and discussions, we recommend the book by Jung [12].”
Hyperstability of the Cauchy equation on restricted domains (2013, background): “, [24,27,33]) we can describe that result simply saying that, for φ(x, y) ≡ c ( ‖x‖ + ‖y‖ ) (with some real c 0 and p < 0), the Cauchy equation (1.”
Ulam’s-Type Stability of First-Order Impulsive Differential Equations with Variable Delay in Quasi–Banach Spaces (2018, background): “Theory of Hyers–Ulam stability mainly developed after the work of Rassias [6] who weakened the condition for the bound of norm of Cauchy difference, which results in a new concept of stability called Hyers–Ulam–Rassias stability; for further detail, see [7] and references cited therein.”
Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation (2018, background): “For the study of functional inequalities concerning the cubic-quadratic-additive equations and a broad variety of other types of functional inequalities, the reader is referred to [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18].”
Stability of higher-order nonlinear impulsive differential equations (2016, background): “For further details and discussion, see the monograph by Jung [11].”
Applications of fixed point theorems to the Hyers-Ulam stability of functional equations–a survey (2012, methodology): “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 ”
On Ulam’s Type Stability of the Linear Equation and Related Issues (2014, background): “For the last 50 years, that issue has been a very popular subject of investigations and we refer the reader to monographs and surveys [7–17] for further information, references, some discussions, and examples of recent results.”
Recent developments of the conditional stability of the homomorphism equation (2015, background): “Ulam’s problem has inspired numerous other authors (for details and further references see [16, 28, 27, 63, 67]); in particular Bourgin, who presented in [15]”
A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers (2014, neutral): “[8, 13, 14, 16, 17, 22, 24, 26]).”
Fixed Point Theory and the Ulam Stability (2014, background): “Our aim is to show connections between different fixed point theorems and the theory of stability, inspired by the problem of Ulam (see [5, 7, 9]).”
Remarks on hyperstability of the Cauchy functional equation (2013, result): “Since then numerous papers on this subject have been published and we refer to [8–10,19,23,26,27,30,31] for more details, some discussions, further references and examples of very recent results.”