共查询到20条相似文献,搜索用时 15 毫秒
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Dong Zhang 《Aequationes Mathematicae》2016,90(3):559-568
We propose a new approach called Hyers–Ulam programming to discriminate whether a generalized linear functional equation, with the form \({\sum_{i=1}^m L_if(\sum_{j=1}^n a_{ij}x_j) = 0}\) for functions from a normed space into a Banach space, has the Hyers–Ulam stability or not. Our main result is that if the induced Hyers–Ulam programming has a solution, then the corresponding functional equation possesses the Hyers–Ulam stability. 相似文献
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Soon-Mo Jung 《Applied Mathematics Letters》2011,24(8):1322-1325
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Aequationes mathematicae - In the present paper by applying the series method we prove the Hyers–Ulam stability of the homogeneous hypergeometric differential equation in a subclass of... 相似文献
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Anna Bahyrycz Krzysztof Ciepliński Jolanta Olko 《Journal of Fixed Point Theory and Applications》2016,18(2):433-444
In this paper we prove, using the fixed point method, the generalized Hyers–Ulam stability of two functional equations in complete non-Archimedean normed spaces. One of these equations characterizes multi-Cauchy–Jensen mappings, and the other gives a characterization of multi-additive-quadratic mappings. 相似文献
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We obtain the infimum of the Hyers–Ulam stability constants for Stancu, Bernstein and Kantorovich operators and prove that in a class of certain positive linear operators this infimum for Bernstein operator has a minimality property. 相似文献
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In this paper, we obtain the general solution and stability of the Jensen-cubic functional equation f((x1+x2)/2, 2y1+y2)+f((x1+x2)/2, 2y1-y2) = f(x1, y1+y2)+f(x1, y1-y2)+6f(x1, y1)+f(x2, y1+y2)+f(x2, y1-y2)+6f(x2, y1). 相似文献
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We prove that Euler’s equation , characterising homogeneous functions, is stable in Hyers–Ulam sense if and only if . 相似文献
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In this paper the following implication is verified for certain basic algebraic curves: if the additive real function f approximately (i.e., with a bounded error) satisfies the derivation rule along the graph of the algebraic curve in consideration, then f can be represented as the sum of a derivation and a linear function. When, instead of the additivity of f, it is assumed that, in addition, the Cauchy difference of f is bounded, a stability theorem is obtained for such characterizations of derivations. 相似文献
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In this paper, we construct a counter example to show that “Theorem” of Hyers–Ulam Stability of Flett’s Point in [M. Das, T. Riedel, P.K. Sahoo, Hyers-Ulam stability of Flett’s points, Applied Mathematics Letters. 16 (3) (2003), 269–271] is incorrect. At the same time, we give the correct theorem and generalize it. 相似文献
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In this paper, we first prove two existence and uniqueness results for fractional-order delay differential equation with respect to Chebyshev and Bielecki norms. Secondly, we prove the above equation is Ulam–Hyers–Mittag-Leffler stable on a compact interval. Finally, two examples are also provided to illustrate our results. 相似文献
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Magdalena Piszczek 《Aequationes Mathematicae》2013,85(1-2):111-118
We prove that a set-valued function satisfying some functional inclusions admits, in appropriate conditions, a unique selection satisfying the corresponding functional equation. As a consequence we obtain the result on the Hyers–Ulam stability of that functional equation. 相似文献
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We show that many general results on Hyers–Ulam stability of some functional equations in a single variable follow immediately from a simple fixed point theorem. The theorem is formulated for self-maps of some subsets of the space of functions from a nonempty set into the set of reals. We also give some applications of that theorem, e.g., in investigations of solutions of some difference equations and functional inequalities. 相似文献
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We prove that the existence of a global prime integral leads, in appropriate conditions, to the Hyers–Ulam stability of a linear partial differential equation of first order. 相似文献
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S.-M. Jung 《Applied Mathematics Letters》2009,22(1):70-74
In this work, we will prove the Hyers–Ulam stability of linear partial differential equations of first order. 相似文献