Mathematical  Culture and Thought

Mathematical Culture and Thought

Document Type : Survey

Subjects

Ansari‎, ‎A‎. ‎H.‎,   ‎Moslehian‎, ‎M‎. ‎S.‎, ‎Refinements of reverse triangle inequalities in inner product spaces‎,  J‎. ‎Inequal‎. ‎Pure Appl‎. ‎Math.‎, 6 (3) (2005)‎, ‎1-12‎.
 
 
‎Birkhoff‎, ‎G.‎, ‎Orthogonality in linear metric spaces‎, Duke‎. ‎Math‎. ‎J.‎, 1 (1935)‎, ‎169--172‎.
 
 
‎Chorianopoulos‎, ‎Ch.‎,  ‎Psarrakos‎, ‎P.‎, ‎Birkhoff-James approximate orthogonality sets and numerical ranges‎, Linear Algebra Appl.‎, 434 (2011)‎, ‎2089--2108‎.
 
 
‎Dadipour F.‎,  ‎Moslehian‎, ‎M‎. ‎S.‎, ‎A characterization of inner product spaces related to the p-angular distance‎, J‎. ‎Math‎. ‎Anal‎. ‎Appl.‎,  371 (2010) (2)‎, ‎677-681‎.
 
 
‎Dadipour‎,  ‎F.‎,  ‎Moslehian‎, ‎M‎. ‎S.‎,  ‎Rassias  J‎. ‎M.‎,   ‎Takahasi‎, ‎S.-E.‎, ‎Characterization of a generalized triangle inequality in normed spaces‎, Nonlinear Anal.-TMA.‎, 75 (2012) (2)‎, ‎735-741‎.
 
 
‎James‎, ‎R‎. ‎C.‎, ‎Orthogonality and linear functionals in normed linear spaces‎, Trans‎. ‎Amer‎. ‎Math‎. ‎Soc.‎, 61 (1947)‎, ‎265--292‎.
 
 
‎James‎, ‎R‎. ‎C.‎, ‎Orthogonality in normed linear spaces‎, Duke‎. ‎Math‎. ‎J.‎, 12 (1945)‎, ‎291--302‎.
 
 
‎Kapoor‎, ‎O‎. ‎P.‎,  ‎Prasad‎, ‎J.‎, ‎Orthogonality and characterizations of inner product spaces‎, Bull‎. ‎Austral‎. ‎Math‎. ‎Soc.‎, 19 (1978)‎, ‎403--416‎.
 
 
‎Moslehian M‎. ‎S.‎,  ‎Zamani‎, ‎A.‎,  ‎Exact and approximate operator parallelism‎, Canad‎. ‎Math‎. ‎Bull.‎, 58 (2015)‎,  ‎207-224‎.
 
 
‎Moslehian M‎. ‎S.‎,  ‎Rassias‎, ‎J‎. ‎M.‎, ‎A characterization of inner product spaces concerning an Euler-Lagrange identity‎, Commun‎. ‎Math‎. ‎Anal.‎, 8 (2010) (2)‎, ‎16-21‎.
 
 
‎Zhi‎, ‎Ch‎. ‎Zh.‎,  ‎Wei‎, ‎L.‎,  ‎L"{u}-Lin‎, ‎L.‎, ‎Projections‎, ‎Birkhoff-orthogonality and angles in normed spaces‎, Commu‎. ‎Math‎. ‎Res.‎, 24 (2011) (4)‎, ‎378--384‎.

  • Receive Date 27 May 2017
  • Publish Date 22 May 2017