Results 21 to 30 of about 8,284,364 (333)

Riemann zeta fractional derivative—functional equation and link with primes

open access: yesAdvances in Differential Equations, 2019
This paper outlines further properties concerning the fractional derivative of the Riemann ζ function. The functional equation, computed by the introduction of the Grünwald–Letnikov fractional derivative, is rewritten in a simplified form that reduces ...
E. Guariglia
semanticscholar   +1 more source

On the Hyers-Ulam-Rassias Stability of a General Quintic Functional Equation and a General Sextic Functional Equation

open access: yesMathematics, 2019
The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation.
Yang-Hi Lee
semanticscholar   +1 more source

On a Functional Equation [PDF]

open access: yesCanadian Mathematical Bulletin, 1979
Let P stand for a polynomial set (p.s.), i.e., a sequence {P0(x), P1(x), P2(x),...} such that for each n P0(x) is a polynomial in x of exact degree n and P0(x)≠0. We refer to Pn(x) as the nth component of P.
Nadhla A. Al-Salam, Waleed A. Al-Salam
openaire   +2 more sources

Solutions and stability of a variant of Wilson's functional equation

open access: yesProyecciones (Antofagasta), 2018
In this paper we will investigate the complex-valued solutions and stability of the generalized variant of Wilson’s functional equation (E) : f(xy) + χ(y)f(σ(y)x) = 2f(x)g(y), x, y ∈ G, where G is a group, σ is an involutive morphism of G and χ is a ...
E. Elqorachi, Ahmed Redouani
semanticscholar   +1 more source

Functional Equations and Fourier Analysis [PDF]

open access: yesCan. Math. Bull. 56 (2013) 218-224, 2010
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.
arxiv   +1 more source

Using Aichinger's equation to characterize polynomial functions [PDF]

open access: yesarXiv, 2022
Aichinger's equation is used to give simple proofs of several well-known characterizations of polynomial functions as solutions of certain functional equations. Concretely, we use that Aichinger's equation characterizes polynomial functions to solve, for arbitrary commutative groups, Ghurye-Olkin's functional equation, Wilson's functional equation, the
arxiv  

On the stability of the linear functional equation in a single variable on complete metric groups [PDF]

open access: yesJournal of Global Optimization, 2014
In this paper we obtain a result on Hyers–Ulam stability of the linear functional equation in a single variable $$f(\varphi (x)) = g(x) \cdot f(x)$$f(φ(x))=g(x)·f(x) on a complete metric group.
Soon-Mo Jung, D. Popa, M. Rassias
semanticscholar   +1 more source

The Numerical Approximation of Nonlinear Functionals and Functional Differential Equations [PDF]

open access: yesPhysics Reports, 18 February 2018, Volume 732, Pages 1-102, 2016
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations) and statistical physics (equations for generating functionals and effective Fokker-Planck equations).
arxiv   +1 more source

Hyperstability of general linear functional equation

open access: yesAequationes Mathematicae, 2016
Our purpose is to investigate criteria for hyperstability of linear type functional equations. We prove that a function satisfying the equation approximately in some sense, must be a solution of it.
A. Bahyrycz, J. Olko
semanticscholar   +1 more source

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