Results 21 to 30 of about 106 (94)
Local stability of the additive functional equation and its applications
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 1, Page 15-26, 2003., 2003 The main purpose of this paper is to prove the Hyers‐Ulam stability of the additive functional equation for a large class of unbounded domains. Furthermore, by using the theorem, we prove the stability of Jensen′s functional equation for a large class of restricted domains.
Soon-Mo Jung, Byungbae Kim
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Stability of a generalized quadratic functional equation in various spaces: a fixed point alternative approach [PDF]
, 2011 Using the fixed point method, we prove the Hyers-Ulam stability of the following quadratic functional equation ...
Hassan Azadi Kenary +3 more
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Notes on stability of the generalized gamma functional equation
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 1, Page 57-63, 2002., 2002 The Hyers‐Ulam stability in three senses is discussed by Kim (2001) for the generalized gamma functional equation g(x + p) = a(x)g(x) under some conditions which involve convergence of complicated series. In this note, those conditions are simplified to be checked easily and more interesting examples other than the classical gamma functional equation ...
Gwang Hui Kim, Bing Xu, Weinian Zhang
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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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A functional equation characterizing cubic polynomials and its stability
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 5, Page 301-307, 2001., 2001 We study the generalized Hyers‐Ulam stability of the functional equation f[x1, x2, x3] = h(x1 + x2 + x3).
Soon-Mo Jung, Prasanna K. Sahoo
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On the stability of generalized gamma functional equation
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 8, Page 513-520, 2000., 2000 We obtain the Hyers‐Ulam stability and modified Hyers‐Ulam stability for the equations of the form g(x + p) = φ(x)g(x) in the following settings: |g(x + p) − φ(x)g(x) | ≤ δ, | g(x + p) − φ(x)g(x) | ≤ ϕ(x), | (g(x + p)/φ(x)g(x)) − 1 | ≤ ψ(x). As a consequence we obtain the stability theorems for the gamma functional equation.
Gwang Hui Kim
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Superstability of functional equations related to spherical functions
Open Mathematics, 2017 In this paper we prove stability-type theorems for functional equations related to spherical functions. Our proofs are based on superstability-type methods and on the method of invariant means.
Székelyhidi László
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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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Pseudo almost periodic solutions for a class of differential equation with delays depending on state
Advances in Nonlinear Analysis, 2019 In this paper, the exponential dichotomy, and Tikhonov and Banach fixed point theorems are used to study the existence and uniqueness of pseudo almost periodic solutions of a class of iterative functional differential equations of the ...
Zhao Hou Yu
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.In this paper, we develop a comprehensive analytical framework for generalized nonlinear, nonhomogeneous Volterra integral equations and fractional differential equations in b‐metric spaces equipped with amorphous binary relations. By introducing an enriched (f, ϕ, ψ, s)‐functional contraction, we extend classical contractive conditions to accommodate ...
D. Srinivasan +2 more
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