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I ‐convexity and Q ‐convexity in Orlicz–Bochner function spaces endowed with the Orlicz norm
Author(s) -
Gong Wanzhong,
Dong Xiaoli,
Wang Kangji
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800268
Subject(s) - convexity , mathematics , norm (philosophy) , banach space , pure mathematics , regular polygon , convex function , uniformly convex space , function (biology) , lp space , mathematical analysis , eberlein–šmulian theorem , geometry , evolutionary biology , political science , financial economics , law , economics , biology
Some characterizations of I ‐convexity and Q ‐convexity of Banach space are obtained. Moreover, the criteria is shown for Orlicz–Bochner function spacesL M ( μ , X )endowed with the Orlicz norm being I ‐convex as well as being Q ‐convex.