Weakly Picard mappings: Retraction-displacement condition, quasicontraction notion and weakly Picard admissible perturbation

By Ioan A. Rus. Studia Universitatis Babeş-Bolyai. Mathematica, 2024

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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. Received 22 October 2023; Accepted 16 November 2023

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fdd4921a15d34ea8f7b7138ecb68f35389fbf542

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Citations in the corpus

Data dependence of the fixed point set of some multivalued weakly Picard operators (2003, background): “[see Rus [22]] If t : X → X is a singlevalued w.”