TY - CHAP
T1 - Quasiconcave functions
AU - Rubshtein, Ben Zion A.
AU - Grabarnik, Genady Ya
AU - Muratov, Mustafa A.
AU - Pashkova, Yulia S.
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - In this chapter we study quasiconcave functions in conjunction with fundamental functions of symmetric spaces. We show that every concave function is also quasiconcave, and conversely, for every quasiconcave function V, there exists its least concave majorant Ṽ, satisfying inequality 1/2≤ V ≤ Ṽ. We also show that fundamental functions of symmetric spaces are quasiconcave.
AB - In this chapter we study quasiconcave functions in conjunction with fundamental functions of symmetric spaces. We show that every concave function is also quasiconcave, and conversely, for every quasiconcave function V, there exists its least concave majorant Ṽ, satisfying inequality 1/2≤ V ≤ Ṽ. We also show that fundamental functions of symmetric spaces are quasiconcave.
UR - http://www.scopus.com/inward/record.url?scp=85006295163&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-42758-4_10
DO - 10.1007/978-3-319-42758-4_10
M3 - Chapter
AN - SCOPUS:85006295163
T3 - Developments in Mathematics
SP - 127
EP - 137
BT - Developments in Mathematics
PB - Springer New York LLC
ER -