Some new estimates of the ‘Jensen gap’

Autor: Shoshana Abramovich, Lars-Erik Persson
Jazyk: angličtina
Rok vydání: 2016
Předmět:
Zdroj: Journal of Inequalities and Applications, Vol 2016, Iss 1, Pp 1-9 (2016)
Druh dokumentu: article
ISSN: 1029-242X
DOI: 10.1186/s13660-016-0985-4
Popis: Abstract Let ( μ , Ω ) $( \mu,\Omega ) $ be a probability measure space. We consider the so-called ‘Jensen gap’ J ( φ , μ , f ) = ∫ Ω φ ( f ( s ) ) d μ ( s ) − φ ( ∫ Ω f ( s ) d μ ( s ) ) $$ J ( \varphi,\mu,f ) = \int_{\Omega}\varphi \bigl( f ( s ) \bigr)\,d\mu ( s ) -\varphi \biggl( \int_{\Omega }f ( s )\,d\mu ( s ) \biggr) $$ for some classes of functions φ. Several new estimates and equalities are derived and compared with other results of this type. Especially the case when φ has a Taylor expansion is treated and the corresponding discrete results are pointed out.
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