Abstract
In this paper, we consider 2-isometries, 2-continuous mappings and mappings preserving equality of 2-distance and investigate the relation between the three mappings in linear 2-normed spaces. We prove that if f: E → F is a mapping preserving equality of 2-distance with its gauge function injective, f is 2-continuous and the range of f contains a segment, then f is affine. Moreover, when dimensionE < 2, the condition that f is 2-continuous could be eliminated. *This work was supported by the National Natural Science Foundation of China, Grant No. 10871101.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
