TY - JOUR
T1 - Some classes of probabilistic inner product spaces and related inequalities
AU - Harikrishnan, Panackal
AU - Guillén, Bernardo Lafuerza
N1 - Publisher Copyright:
© 2020 Tusi Mathematical Research Group (TMRG).
PY - 2020/6/1
Y1 - 2020/6/1
N2 - We give a new definition for probabilistic inner product spaces, which is sufficiently general to encompass the most important class of proba-bilistic inner product spaces (briefly, PIP spaces). We have established certain classes of PIP spaces and especially, illustrated that how to construct a real inner product from a Menger PIP space. Finally, we have established the analogous of Cauchy{Schwarz inequality in this general PIP spaces.
AB - We give a new definition for probabilistic inner product spaces, which is sufficiently general to encompass the most important class of proba-bilistic inner product spaces (briefly, PIP spaces). We have established certain classes of PIP spaces and especially, illustrated that how to construct a real inner product from a Menger PIP space. Finally, we have established the analogous of Cauchy{Schwarz inequality in this general PIP spaces.
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U2 - 10.22034/kjm.2020.109815
DO - 10.22034/kjm.2020.109815
M3 - Article
AN - SCOPUS:85088576171
SN - 2423-4788
VL - 6
SP - 180
EP - 192
JO - Khayyam Journal of Mathematics
JF - Khayyam Journal of Mathematics
IS - 2
ER -