Results 11 to 20 of about 502 (93)
Fuzzy approximation of an additive functional equation
Journal of Function Spaces, Volume 9, Issue 2, Page 205-215, 2011., 2011 In this paper, we investigate the generalized Hyers– Ulam– Rassias stability of the functional equation ∑i=1mf(mxi+∑j=1, j≠imxj)+f(∑i=1mxi)=2f(∑i=1mmxi) in fuzzy Banach spaces and some applications of our results in the stability of above mapping from a normed space to a Banach space will be exhibited.
G. Zamani Eskandani +3 more
wiley +1 more source
The Jensen functional equation in non‐Archimedean normed spaces
Journal of Function Spaces, Volume 7, Issue 1, Page 13-24, 2009., 2009 We investigate the Hyers–Ulam–Rassias stability of the Jensen functional equation in non‐Archimedean normed spaces and study its asymptotic behavior in two directions: bounded and unbounded Jensen differences. In particular, we show that a mapping f between non‐Archimedean spaces with f(0) = 0 is additive if and only if ‖f(x+y2)−f(x)+f(y)2‖→0 as max ...
Mohammad Sal Moslehian, George Isac
wiley +1 more source
Matrix method for solving linear complex vector functional equations
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 4, Page 217-238, 2002., 2002 We give a new matrix method for solving both homogeneous and nonhomogeneous linear complex vector functional equations with constant complex coefficients.
Ice B. Risteski
wiley +1 more source
On the stability of the quadratic mapping in normed spaces
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 4, Page 217-229, 2001., 2001 The Hyers‐Ulam stability, the Hyers‐Ulam‐Rassias stability, and also the stability in the spirit of Gavruţa for each of the following quadratic functional equations f(x + y) + f(x − y) = 2f(x) + 2f(y), f(x + y + z) + f(x − y) + f(y − z) + f(z − x) = 3f(x) + 3f(y) + 3f(z), f(x + y + z) + f(x) + f(y) + f(z) = f(x + y) + f(y + z) + f(z + x) are ...
Gwang Hui Kim
wiley +1 more source
Quadratic functional equations of Pexider type
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 5, Page 351-359, 2000., 2000 First, the quadratic functional equation of Pexider type will be solved. By applying this result, we will also solve some functional equations of Pexider type which are closely associated with the quadratic equation.
Soon-Mo Jung
wiley +1 more source
On a modified Hyers‐Ulam stability of homogeneous equation
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 3, Page 475-478, 1998., 1998 In this paper, a generalized Hyers‐Ulam stability of the homogeneous equation shall be proved, i.e., if a mapping f satisfies the functional inequality ‖f(yx) − ykf(x)‖ ≤ φ(x, y) under suitable conditions, there exists a unique mapping T satisfying T(yx) = ytT(x) and ‖T(x) − f(x)‖ ≤ Φ(x).
Soon-Mo Jung
wiley +1 more source
Functional Equations and Fourier Analysis
, 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 ...
Akkouchi +5 more
core +1 more source
On the Orthogonal Stability of the Pexiderized Quadratic Equation
, 2005 The Hyers--Ulam stability of the conditional quadratic functional equation of Pexider type f(x+y)+f(x-y)=2g(x)+2h(y), x\perp y is established where \perp is a symmetric orthogonality in the sense of Ratz and f is odd.Comment: 10 pages, Latex; Changed ...
Aczél J. +12 more
core +2 more sources
Hyers-Ulam stability of exact second-order linear differential equations [PDF]
, 2012 In this article, we prove the Hyers-Ulam stability of exact second-order linear differential equations. As a consequence, we show the Hyers-Ulam stability of the following equations: second-order linear differential equation with constant coefficients ...
Badrkhan Alizadeh +3 more
core +1 more source
On a functional equation that has the quadratic-multiplicative property
Open Mathematics, 2020 In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation:ϕ(st−uv)+ϕ(sv+tu)=[ϕ(s)+ϕ(u)][ϕ(t)+ϕ(v)]\phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v ...
Park Choonkil +4 more
doaj +1 more source