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Authors: IOAN A. RUS.
Received 22 October 2023; Accepted 16 November 2023. Published Online: 2024-03-20
Published Print: 2024-03-30
pp. 211-221
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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.
Keywords: Metric space, fixed point equation, Picard mapping, weakly Picard mapping, admissible perturbation, retraction-displacement condition, data dependence estimate, Ulam-Hyers stability, well-posedness, Ostrowski property, quasicontraction.
