Results 1 to 10 of about 4,706,970 (298)

On a Functional Equation of Ruijsenaars

Theoretical and Mathematical Physics, 2002
We obtain the general solution of the functional equation introduced by Ruijsenaars guaranteeing the commutativity of n operators associated with the quantum Ruijsenaars-Schneider models.
Byatt-Smith, J. G. B., Braden, H. W.
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Cauchy type functional equations related to some associative rational functions

Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2019
L. Losonczi [4] determined local solutions of the generalized Cauchy equation f(F(x, y))= f(x) + f(y) on components of the denition of a given associative rational function F. The class of the associative rational function was described by A. Chéritat [1]
Katarzyna Domańska
doaj  

Stability of generalized Newton difference equations

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2012
In the paper we discuss a stability in the sense of the generalized Hyers-Ulam-Rassias for functional equations Δn(p, c)φ(x) = h(x), which is called generalized Newton difference equations, and give a sufficient condition of the generalized Hyers-Ulam ...
Wang Zhihua, Shi Yong-Guo
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ON STABILILTY OF GENERALIZED ADDITIVE FUNCTIONAL EQUATIONS IN BANACH SPACE

Academy Journal of Science and Engineering
The stability problem arises when a functional equation is replaced by an inequality. When the equation admits a unique solution, we say that the equation is stable. In this paper, an Arunkumar-Agilan type additive functional equation is considered.
Yusuf Ibrahim, Aminu A. Usman
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The Cotangent Function as an Avatar of the Polylogarithm Function of Order 0 and Ramanujan’s Formula

Axioms
In this paper we will be concerned with zeta-symmetry—the functional equation for the (Riemann) zeta-function (equivalents to which are called modular relations)—and reveal the reason why so many results are intrinsic to PFE (Partial Fraction Expansion ...
Ruiyang Li, Haoyang Lu, Shigeru Kanemitsu   +2 more
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On Hecke’s functional equation [PDF]

Bulletin of the American Mathematical Society, 1961
Chandrasekharan, K., Narasimhan, Raghavan   +1 more
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Hyers–Ulam Stability of a Multi-Variable Additive-Quadratic Functional Equation

Mathematics
In this paper, we investigate the generalized Hyers–Ulam stability of a multi-variable additive-quadratic functional equation in Banach spaces. Unlike traditional mixed-type equations that segregate variables, the proposed equation embeds a dense ...
Jae-Hyeong Bae, Won-Gil Park
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Functional Equations with an Anti-Endomorphism for Functions with Multidimensional Codomains

Annales Mathematicae Silesianae
Let S be a semigroup, ℍ be the skew field of quaternions, and ψ: S → S be an anti-endomorphism. We determine the general solution of the functional equation g(xy)-g(xψ(y))=2g(x)g(y),          x, y∈S,g\left( {xy} \right) - g\left( {x\psi \left( y \right)}
Ouhabi Ayoub, Zeglami Driss, Ayoubi Mohamed   +2 more
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A fixed-point approach to the stability of a functional equation on quadratic forms

Journal of Inequalities and Applications, 2011
Using the fixed-point method, we prove the generalized Hyers-Ulam stability of the functional equation f ( x + y , z + w ) + f ( x - y , z - w ) = 2 f ( x , z ) + 2 f ( y , w ) . The quadratic form f : ℝ × ℝ → &#
Park Won-Gil, Bae Jae-Hyeong
doaj  

On the Functional Equation [PDF]

Proceedings of the National Academy of Sciences, 1947
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