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- W56914456 startingPage "193" @default.
- W56914456 abstract "For a convex subset ∆ of a real vector space X and a function f: ∆ → ℝ, the homogeneity set Hf is defined by <m:math display='block'><m:mrow><m:msub><m:mrow><m:mi>H</m:mi></m:mrow><m:mrow><m:mi>f</m:mi></m:mrow></m:msub><m:mo>:</m:mo><m:mo>=</m:mo><m:mfenced open='{' close='}'><m:mrow><m:mrow><m:mi>λ</m:mi><m:mo>∈</m:mo><m:mfenced open='[' close=']'><m:mrow><m:mrow><m:mn>0</m:mn><m:mo>,</m:mo><m:mn>1</m:mn></m:mrow></m:mrow></m:mfenced><m:mo>:</m:mo><m:mi>f</m:mi><m:mfenced open='(' close=')'><m:mrow><m:mrow><m:mi>λ</m:mi><m:mi>x</m:mi><m:mo>+</m:mo><m:mfenced open='(' close=')'><m:mrow><m:mrow><m:mn>1</m:mn><m:mo>−</m:mo><m:mi>λ</m:mi></m:mrow></m:mrow></m:mfenced><m:mi>y</m:mi></m:mrow></m:mrow></m:mfenced><m:mo>≤</m:mo><m:mi>λ</m:mi><m:mi>f</m:mi><m:mfenced open='(' close=')'><m:mrow><m:mi>x</m:mi></m:mrow></m:mfenced><m:mo>+</m:mo><m:mfenced open='(' close=')'><m:mrow><m:mrow><m:mn>1</m:mn><m:mo>−</m:mo><m:mi>λ</m:mi></m:mrow></m:mrow></m:mfenced><m:mi>f</m:mi><m:mfenced open='(' close=')'><m:mrow><m:mi>y</m:mi></m:mrow></m:mfenced><m:mtext> </m:mtext><m:mi>f</m:mi><m:mi>o</m:mi><m:mi>r</m:mi><m:mtext> </m:mtext><m:mi>a</m:mi><m:mi>l</m:mi><m:mi>l</m:mi><m:mtext> </m:mtext><m:mi>x</m:mi><m:mo>,</m:mo><m:mi>y</m:mi><m:mtext> </m:mtext><m:mo>∈</m:mo><m:mtext> </m:mtext><m:mi>Δ</m:mi></m:mrow></m:mrow></m:mfenced></m:mrow></m:math>> $$ {H_{f}}: = left{ {lambda in left[ {0,1} right]:fleft( {lambda x + left( {1 - lambda } right)y} right) le lambda fleft( x right) + left( {1 - lambda } right)fleft( y right){kern 1pt} for{kern 1pt} all{kern 1pt} x,y{kern 1pt} in {kern 1pt} Delta } right} $$ . In this paper, homogeneity sets of Jensen-convex functions are discussed." @default.
- W56914456 created "2016-06-24" @default.
- W56914456 creator A5027555035 @default.
- W56914456 date "1980-01-01" @default.
- W56914456 modified "2023-09-25" @default.
- W56914456 title "Homogeneity Sets for Jensen-Convex Functions" @default.
- W56914456 cites W2004177906 @default.
- W56914456 cites W2048305092 @default.
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- W56914456 doi "https://doi.org/10.1007/978-3-0348-6324-7_20" @default.
- W56914456 hasPublicationYear "1980" @default.
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