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OSTROWSKI TYPE INEQUALITY FOR ABSOLUTELY CONTINUOUS FUNCTIONS ON SEGMENTS IN LINEAR SPACES
Kikianty, Eder,Dragomir, Sever S.,Cerone, Pietro Korean Mathematical Society 2008 대한수학회보 Vol.45 No.4
An Ostrowski type inequality is developed for estimating the deviation of the integral mean of an absolutely continuous function, and the linear combination of its values at k + 1 partition points, on a segment of (real) linear spaces. Several particular cases are provided which recapture some earlier results, along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Some inequalities are obtained by applying these results for semi-inner products; and some of these inequalities are proven to be sharp.
Ostrowski type inequality for absolutely continuous functions on segments in linear spaces
Eder Kikianty,Sever S. Dragomir,Pietro Cerone 대한수학회 2008 대한수학회보 Vol.45 No.4
An Ostrowski type inequality is developed for estimating the deviation of the integral mean of an absolutely continuous function, and the linear combination of its values at k + 1 partition points, on a segment of (real) linear spaces. Several particular cases are provided which recapture some earlier results, along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Some inequalities are obtained by applying these results for semi-inner products; and some of these inequalities are proven to be sharp An Ostrowski type inequality is developed for estimating the deviation of the integral mean of an absolutely continuous function, and the linear combination of its values at k + 1 partition points, on a segment of (real) linear spaces. Several particular cases are provided which recapture some earlier results, along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Some inequalities are obtained by applying these results for semi-inner products; and some of these inequalities are proven to be sharp
THREE GEOMETRIC CONSTANTS FOR MORREY SPACES
Gunawan, Hendra,Kikianty, Eder,Sawano, Yoshihiro,Schwanke, Christopher Korean Mathematical Society 2019 대한수학회보 Vol.56 No.6
In this paper we calculate three geometric constants, namely the von Neumann-Jordan constant, the James constant, and the Dunkl-Williams constant, for Morrey spaces and discrete Morrey spaces. These constants measure uniformly nonsquareness of the associated spaces. We obtain that the three constants are the same as those for $L^1$ and $L^{\infty}$ spaces.
Three geometric constants for Morrey spaces
Hendra Gunawan,Eder Kikianty,Yoshihiro Sawano,Christopher Schwanke 대한수학회 2019 대한수학회보 Vol.56 No.6
In this paper we calculate three geometric constants, namely the von Neumann-Jordan constant, the James constant, and the Dunkl-Williams constant, for Morrey spaces and discrete Morrey spaces. These constants measure uniformly nonsquareness of the associated spaces. We obtain that the three constants are the same as those for $L^1$ and $L^\infty$ spaces.