Generalizations and applications of Young’s integral inequality by higher order derivatives

Journal of Inequalities and Applications

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[1] 0000 0000 8645 6375, grid.412097.9, School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, China;0000 0000 9870 9448, grid.440709.e, College of Mathematical Sciences, Dezhou University, Dezhou, Shandong, China;grid.410561.7, School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin, China;0000 0000 8547 6673, grid.411647.1, College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, China;

关键词: Young’s integral inequality;    Inverse function;    Taylor’s theorem;    Higher order derivative;    Lebesgue measure;    Norm;    Application;    Exponential integral;    Logarithmic integral;    Existence of partitions of unity;    26D15;    26A42;    26A48;    26A51;    26D05;    26D07;    33B10;    33B20;    41A58;   

DOI  :  10.1186/s13660-019-2196-2

来源: publisher

【 摘 要 】

In the paper, the authors generalize Young’s integral inequality via Taylor’s theorems in terms of higher order derivatives and their norms, andapply newly-established integral inequalities to estimate several concrete definite integrals, including a definite integral of a function which plays an indispensable role in differential geometry and has a connection with the Lah numbers in combinatorics, the exponential integral, and the logarithmic integral.

【 授权许可】

CC BY