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引用次数: 61
摘要
假设 (X, d) 是一个度量空间，f : X → X 是一个映射，G(-, f (-)) 是 f 的可允许扰动：在对 f 和 G 施加的条件中，我们有以下条件：（DDE）映射 f 扰动的数据依赖性估计；（UH）方程 x = f (x) 的 Ulam-Hyers 稳定性；（WP）f 的定点问题的好求性；（OP）映射 f 的 Ostrowski 特性。提出了一些研究方向：47H25, 54H25, 47H09, 65J15, 37N30, 39A30.Received 22 October 2023; Accepted 16 November 2023.
Let (X, d) be a metric space, f : X → X be a mapping and G(·, f (·)) be an admissible perturbation of f. In this paper we study the following problems: In which conditions imposed on f and G we have the following:
(DDE) data dependence estimate for the mapping f perturbation;
(UH) Ulam-Hyers stability for the equation, x = f (x);
(WP) well-posedness of the fixed-point problem for f;
(OP) Ostrowski property of the mapping f.
Some research directions are suggested.
Mathematics Subject Classification (2010): 47H25, 54H25, 47H09, 65J15, 37N30, 39A30.
Received 22 October 2023; Accepted 16 November 2023
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