Results 11 to 20 of about 722 (111)
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
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A Parametric Functional Equation Originating from Number Theory
Annales Mathematicae Silesianae, 2022 Let S be a semigroup and α, β ∈ ℝ. The purpose of this paper is to determine the general solution f : ℝ2 → S of the following parametric functional equation f(x1+x2+αy1y2,x1y2+x2y1+βy1y2)=f(x1,y1)f(x2,y2),f\left( {{x_1} + {x_2} + \alpha {y_1}{y_2},{x_1 ...
Mouzoun Aziz +2 more
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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
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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
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The Ulam Stability Problem for the Functional Equation f(x * g(y)) = f(x) f(y) [PDF]
, 2020 We present a solution of Ulam’s stability problem for the functional equation f(x * g(y)) = f(x)f(y) with vector-valued map f. Mathematics Subject Classification.
Badora, Roman
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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 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
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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
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New Pexiderizations of Drygas’ Functional Equation on Abelian Semigroups
Annales Mathematicae Silesianae, 2023 Let (S, +) be an abelian semigroup, let (H, +) be an abelian group which is uniquely 2-divisible, and let ϕ be an endomorphism of S. We find the solutions f, h : S → H of each of the functional equations f(x+y)+f(x+ϕ(y))=h(x)+f(y)+f∘ϕ(y), x,y∈S,f(x+y)+f ...
Aissi Youssef, Zeglami Driss
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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