Results 11 to 20 of about 94 (84)
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
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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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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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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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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
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International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.In this paper, we introduce a new concept called mixed 3D‐Jensen and additive functional equations FEs. In the following, we demonstrate that they are additive mappings and we show that they can be C‐linear. After that, we define triple homoderivations under the above condition on triple Banach algebras (TBAs).
Iman Bahreini +2 more
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Study on Approximate C∗‐Bimultiplier and JC∗‐Bimultiplier in C∗‐Ternary Algebra
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.An additive‐quadratic mapping F:A×A⟶B is one that adheres to the following equations: Fr+s,t=Fr,t+Fs,t,Fr,s+t+Fr,s−t=22Fr,s+Fr,t. This paper leverages the fixed‐point method to investigate C∗‐bimultiplier and JC∗‐bimultiplier approximations on C∗‐ternary algebras. The focus is on the additive‐quadratic functional equation: Fr+s,t+u+Fr+s,t−u=2222Fr,t+Fr,
Mina Mohammadi +3 more
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On Approximations of a System of Functional Equations Having Monomials
Journal of Function Spaces, Volume 2026, Issue 1, 2026.We use an s‐monomial to define the multimonomial mappings as a system of functional equations having monomials. The main contribution of the paper is twofold. First, we give a representation of such new multiple variable mappings as a unified equation, thereby providing a complete characterization.
Siriluk Donganont +2 more
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Stability and Superstability of a Linear Functional Equation on Restricted Domains
Journal of Function Spaces, Volume 2026, Issue 1, 2026.This paper investigates the Hyers–Ulam stability and superstability of the functional equation f(x2 + yf(z)) = xf(x) + zf(y) for real‐valued functions f : R⟶R on some restricted subsets of R.
Abbas Najati +3 more
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