caa a22 4500 465825435 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02112278 doi (NATIONALLICENCE)springer-10.1007/BF02112278 Jensen inequalities for functions with higher monotonicities [Elektronische Daten] [A. Fink, M. Jodeit Jr] Summary: We investigate generalizations of the classical Jensen and Chebyshev inequalities. On one hand, we restrict the class of functions and on the other we enlarge the class of measures which are allowed. As an example, consider the inequality (J)ϕ(∫f(x) dμ) ⩽ A ∫ ϕ(f(x) dμ, d∫ dμ = 1. Iff is an arbitrary nonnegativeL x function, this holds ifμ ⩾ 0,ϕ is convex andA = 1. Iff is monotone the measure μ need not be positive for (J) to hold for all convex ϕ withA = 1. If ϕ has higher monotonicity, e.g., ϕ′ is also convex, then we get a version of (J) withA < 1 and measures μ that need not be positive. Birkhäuser Verlag, 1990 Primary 26D15, 26D20 nationallicence Fink A. Department of Mathematics, Iowa State University, 50011, Ames, IA, USA aut Jodeit Jr M. Department of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA aut aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 26-43 0001-9054 40:1<26 1990 40 10 https://doi.org/10.1007/BF02112278 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02112278 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fink A. Department of Mathematics, Iowa State University, 50011, Ames, IA, USA aut NATIONALLICENCE 700 1- Jodeit Jr M. Department of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 26-43 0001-9054 40:1<26 1990 40 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer