norm derivatives
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2021 ◽  
Vol 12 (3) ◽  
Author(s):  
Divya Khurana ◽  
Debmalya Sain

2018 ◽  
Vol 70 (2) ◽  
pp. 379-393 ◽  
Author(s):  
Ali Zamani ◽  
Mohammad Sal Moslehian

Abstract We introduce the relation ρλ-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives and present some of its essential properties. Among other things, we give a characterization of inner product spaces via the functional ρλ. Moreover, we consider a class of linear mappings preserving this new kind of orthogonality. In particular, we show that a linear mapping preserving ρλ-orthogonality has to be a similarity, that is, a scalar multiple of an isometry.


2018 ◽  
Vol 93 (4) ◽  
pp. 651-667 ◽  
Author(s):  
Mahdi Dehghani ◽  
Mohammed Abed ◽  
Ruhollah Jahanipur

10.1142/7452 ◽  
2009 ◽  
Author(s):  
Claudi Alsina ◽  
Justyna Sikorska ◽  
M Santos Tomás

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