Results 11 to 20 of about 767 (107)
Hyers-Ulam-Rassias Stability of Generalized Derivations [PDF]
, 2006 The generalized Hyers--Ulam--Rassias stability of generalized derivations on unital Banach algebras into Banach bimodules is established.Comment: 9 pages, minor changes, to appear in Internat. J. Math.
Moslehian, Mohammad Sal
core +5 more sources
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
On the commutation of generalized means on probability spaces [PDF]
, 2016 Let $f$ and $g$ be real-valued continuous injections defined on a non-empty real interval $I$, and let $(X, \mathscr{L}, \lambda)$ and $(Y, \mathscr{M}, \mu)$ be probability spaces in each of which there is at least one measurable set whose measure is ...
Leonetti, Paolo +2 more
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The stability of an additive (ρ_1, ρ_2)-functional inequality in Banach spaces
Journal of Mathematical Inequalities, 2019 In this paper, we introduce and solve the following additive (ρ1,ρ2) -functional inequality ‖ f (x+ y)− f (x)− f (y)‖ ‖ρ1( f (x+ y)+ f (x− y)−2 f (x))‖ (1) + ∥∥∥ρ2 ( 2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ , where ρ1 and ρ2 are fixed nonzero complex numbers ...
Choonkill Park
semanticscholar +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
Euler-Lagrange radical functional equations with solution and stability
, 2020 In this article, we introduce the generalized Euler-Lagrange radical functional equations of type sextic and quintic. Also, we obtain their general solution and investigate the generalized Hyers-Ulam-Rassias stability in modular spaces using fixed point ...
Murali Ramdoss +2 more
semanticscholar +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
Approximate multi-variable bi-Jensen-type mappings
Demonstratio Mathematica, 2023 In this study, we obtained the stability of the multi-variable bi-Jensen-type functional equation: n2fx1+⋯+xnn,y1+⋯+ynn=∑i=1n∑j=1nf(xi,yj).{n}^{2}f\left(\frac{{x}_{1}+\cdots +{x}_{n}}{n},\frac{{y}_{1}+\cdots +{y}_{n}}{n}\right)=\mathop{\sum }\limits_{i=1}
Bae Jae-Hyeong, Park Won-Gil
doaj +1 more source