• Title/Summary/Keyword: G$\hat{a}$teaux derivatives

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Improvement of Jensen's Inequality in terms of Gâteaux Derivatives for Convex Functions in Linear Spaces with Applications

  • Khan, Muhammad Adil;Khalid, Sadia;Pecaric, Josip
    • Kyungpook Mathematical Journal
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    • v.52 no.4
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    • pp.495-511
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    • 2012
  • In this paper, we prove some inequalities in terms of G$\hat{a}$teaux derivatives for convex functions defined on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give applications for norms, mean $f$-deviations and $f$-divergence measures.

BEST APPROXIMATION SETS IN LINEAR 2-NORMED SPACES

  • Elumalai, S.;Cho, Y.J.;Kim, S.S
    • Communications of the Korean Mathematical Society
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    • v.12 no.3
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    • pp.619-629
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    • 1997
  • In this paper, we give some properties of the sets $D_z(x_o, G)P_{G, z}(x)$. We also provide the relation between $P_{G, z}(x)$ and G$\hat{a}$teaux derivatives.

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