Results 11 to 20 of about 70 (62)
The stability of functional equation min{
Journal of Inequalities and Applications, 2011 In this paper, we prove the stability of the functional equation min {f(x + y), f(x - y)} = |f(x) - f(y)| in the class of real, continuous functions of real variable.
Przebieracz Barbara
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Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces [PDF]
Journal of Inequalities and Applications, 2011 Lex X be a normed space and Y be a Banach fuzzy space. Let D = {(x, y) ∈ X × X : ||x|| + ||y|| ≥ d} where d > 0. We prove that the Pexiderized Jensen functional equation is stable in the fuzzy norm for functions defined on D and ...
Kang Jung Im, Cho Yeol Je, Najati Abbas
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On the Ulam-Hyers stability of a quadratic functional equation [PDF]
Journal of Inequalities and Applications, 2011 The Ulam-Hyers stability problems of the following quadratic equation r 2 f x + y r + r 2 f x - y r = 2 f ( x ) + 2 f ( y ) , where r is a nonzero rational number, shall be treated.
Park Won-Gil +2 more
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On singular nonlinear distributional and impulsive initial and boundary value problems [PDF]
Boundary Value Problems, 2011 Purpose To derive existence and comparison results for extremal solutions of nonlinear singular distributional initial value problems and boundary value problems.
Heikkilä Seppo
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A maximum theorem for generalized convex functions [PDF]
, 2022 Motivated by the Maximum Theorem for convex functions (in the setting of linear spaces) and for subadditive functions (in the setting of Abelian semigroups), we establish a Maximum Theorem for the class of generalized convex functions, i.e., for ...
PÁLES, Zsolt
core +1 more source
Linear differential equations with unbounded delays and a forcing term
Abstract and Applied Analysis, Volume 2004, Issue 4, Page 337-345, 2004., 2004 The paper discusses the asymptotic behaviour of all solutions of the differential equation y˙(t)=−a(t)y(t)+∑i=1nbi(t)y(τi(t))+f(t), t ∈ I = [t0, ∞), with a positive continuous function a, continuous functions bi, f, and n continuously differentiable unbounded lags.
Jan Čermák, Petr Kundrát
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Ill‐posed equations with transformed argument
Abstract and Applied Analysis, Volume 2003, Issue 13, Page 785-791, 2003., 2003 We discuss the operator transforming the argument of a function in the L2‐setting. Here this operator is unbounded and closed. For the approximate solution of ill‐posed equations with closed operators, we present a new view on the Tikhonov regularization.
Simone Gramsch, Eberhard Schock
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On local properties of compactly supported solutions of the two‐coefficient dilation equation
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 3, Page 139-148, 2002., 2002 Let a and b be reals. We consider the compactly supported solutions φ : ℝ → ℝ of the two‐coefficient dilation equation φ(x) = aφ(2x) + bφ(2x − 1). In this paper, we determine sets Ba,b, Ca,b, and Za,b defined in the following way: let x ∈ [0, 1]. We say that x ∈ Ba,b (resp., x ∈ Ca,b, x ∈ Za,b) if the zero function is the only compactly supported ...
Janusz Morawiec
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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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A Gauss type functional equation
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 9, Page 565-569, 2001., 2001 Gauss′ functional equation (used in the study of the arithmetic‐geometric mean) is generalized by replacing the arithmetic mean and the geometric mean by two arbitrary means.
Silvia Toader +2 more
wiley +1 more source