On the Stability of Orthogonal Additivity in $\beta$-Homogeneous $F$-Spaces
Received:March 27, 2021  Revised:January 11, 2022
Key Word: Hyers-Ulam stability   $\beta$-homogeneous $F$-spaces   quasi-Banach spaces   orthogonal additivity  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11971493; 12071491) and the Fundamental Research Funds for the Central Universities (Grant No.2021qntd21).
Author NameAffiliation
Qi LIU Department of Mathematics, Sun Yat-sen University, Guangdong 510275, P. R. China 
Linlin FU Department of Mathematics, Sun Yat-sen University, Guangdong 510275, P. R. China 
Yongjin LI Department of Mathematics, Sun Yat-sen University, Guangdong 510275, P. R. China 
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Abstract:
      In this paper, we study the stability of the orthogonal equation, which is closely related to the results by W. Fechner and J. Sikorska in 2010. There are some differences that we consider the target space with the $\beta$-homogeneous norm and quasi-norm. Overcoming the $\beta$-homogeneous norm and quasi-norm bottlenecks, we get some new results.
Citation:
DOI:10.3770/j.issn:2095-2651.2022.03.007
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