{"title":"Weakly Picard mappings: Retraction-displacement condition, quasicontraction notion and weakly Picard admissible perturbation","authors":"I. Rus","doi":"10.24193/subbmath.2024.1.13","DOIUrl":null,"url":null,"abstract":"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:\n(DDE) data dependence estimate for the mapping f perturbation; \n(UH) Ulam-Hyers stability for the equation, x = f (x);\n(WP) well-posedness of the fixed-point problem for f; \n(OP) Ostrowski property of the mapping f.\nSome research directions are suggested.\nMathematics Subject Classification (2010): 47H25, 54H25, 47H09, 65J15, 37N30, 39A30.\nReceived 22 October 2023; Accepted 16 November 2023","PeriodicalId":517948,"journal":{"name":"Studia Universitatis Babes-Bolyai Matematica","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"61","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Universitatis Babes-Bolyai Matematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/subbmath.2024.1.13","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 61
Abstract
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
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.
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