Fixed Points and Generalized Hyers-Ulam Stability
By Liviu Cadariu, L. Gǎvruţa, P. Gǎvruţa. 2012
79 citations recorded by the source corpus.
In this paper we prove a fixed-point theorem for a class of operators with suitable properties, in very general conditions. Also, we show that some recent fixed-points results in Brzdek et al., (2011) and Brzdek and Cieplinski (2011) can be obtained directly from our theorem. Moreover, an affirmative answer to the open problem of Brzdek and Cieplinski (2011) is given. Several corollaries, obtained directly from our main result, show that this is a useful tool for proving properties of generalized Hyers-Ulam stability for some functional equations in a single variable.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/114f5c58a07f03f8e52bbb6568a6ef4d6b974abf
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Janusz Brzdek
- Krzysztof Cieplinski
- Liviu Cadariu
- Justyna Sikorska
- Wlodzimierz Fechner
- Mohammad Sal Moslehian
Citations in the corpus
- Hyperstability and Superstability (2013, background): “The hyperstability results that we have presented so far have been obtained through the fixed point theorem from [34] (see also [35, 36]; cf.”
- Fixed Point Theory and the Ulam Stability (2014, background): “A slightly improved version of this outcome was obtained in [66] in response to an open problem concerning the uniqueness of the mappingψ, defined below.”