Richard’s inequality, Cauchy–Schwarz’s inequality, and approximate solutions of Sincov’s equation
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Abstract:
We observe a connection between Cauchy–Schwarz’s and Richard’s inequalities in inner product spaces and a Ulam-type stability problem for the multiplicative Sincov functional equation. We prove that this equation is superstable for unbounded mappings, i.e., every unbounded approximate solution is an exact solution.References
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Additional Information
- Włodzimierz Fechner
- Affiliation: Institute of Mathematics, Łódź University of Technology, ul. Wólczańska 215, 90-924 Łódź, Poland
- Email: wlodzimierz.fechner@p.lodz.pl
- Received by editor(s): July 31, 2018
- Received by editor(s) in revised form: January 13, 2019
- Published electronically: April 18, 2019
- Additional Notes: The work performed in this study was supported by the National Science Centre, Poland (under Grant No. 2015/19/B/ST6/03259).
- Communicated by: Stephen Dilworth
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3955-3960
- MSC (2010): Primary 26D15, 39B62, 39B82, 46C05
- DOI: https://doi.org/10.1090/proc/14543
- MathSciNet review: 3993788