分形集上广义s-凸函数的一类带有局部分数积分的Hadamard不等式及应用
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摘要
利用局部分数积分的分析方法,给出分形集上广义s-凸函数的Hadamard型恒等式,进而得到一类Hadamard不等式,并结合数值积分及几个常用的平均值给出其应用.
By using the analytical method of local fractional integrals,we gave a Hadamard type identity of generalized s-convex functions on fractal sets,and then obtained a class of Hadamard inequalities,some applications were given by combining numerical integration and several special means.
By using the analytical method of local fractional integrals,we gave a Hadamard type identity of generalized s-convex functions on fractal sets,and then obtained a class of Hadamard inequalities,some applications were given by combining numerical integration and several special means.
引文
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[2]孙文兵.映射导数为s-凸函数且在分数次积分下的Hadamard型不等式[J].吉林大学学报(理学版),2017,55(4):809-814.(SUN Wenbing.Hadamard-Type Inequalities with Mapping Derivatives Being s-Convex Functions and under Fractional Integrals[J].Journal of Jilin University(Science Edition),2017,55(4):809-814.)
[3]QIU Ke’e,WANG Jinrong.A Fractional Integral Identity and Its Application to Fractional Hermite-Hadamard Type Inequalities[J].J Interdis Math,2018,21(1):1-16.
[4]BABAKHANI A,DAFTARDAR-GEJJI V.On Calculus of Local Fractional Derivatives[J].J Math Anal Appl,2002,270(1):66-79.
[5]YANG Xiaojun.Advanced Local Fractional Calculus and Its Applications[M].New York:World Science Publisher,2012.
[6]GOLMANKHANEH A K,YANG Xiaojun,BALEANU D.Einstein Field Equations within Local Fractional Calculus[J].Roman J Phy,2015,60(2):22-31.
[7]MO Huixia,SUI Xin,YU Dongyan.Generalized Convex Functions on Fractal Sets and Two Related Inequalities[J/OL].Abstract Appl Anal,2014-06-15.http://dx.doi.org/10.1155/2014/636751.
[8]GRADSHTEYN I S,RYZHIK I M.Tables of Integrals,Series and Products[M].San Diego:Academic Press,2000.
[9]孙文兵.分形空间上的新Hadamard型不等式及应用[J].华东师范大学学报(自然科学版),2017(6):33-41.(SUN Wenbing.New Hadamard-Type Inequalities on Fractal Space and Their Applications[J].Journal of East China Normal University(Natural Science),2017(6):33-41.)
[2]孙文兵.映射导数为s-凸函数且在分数次积分下的Hadamard型不等式[J].吉林大学学报(理学版),2017,55(4):809-814.(SUN Wenbing.Hadamard-Type Inequalities with Mapping Derivatives Being s-Convex Functions and under Fractional Integrals[J].Journal of Jilin University(Science Edition),2017,55(4):809-814.)
[3]QIU Ke’e,WANG Jinrong.A Fractional Integral Identity and Its Application to Fractional Hermite-Hadamard Type Inequalities[J].J Interdis Math,2018,21(1):1-16.
[4]BABAKHANI A,DAFTARDAR-GEJJI V.On Calculus of Local Fractional Derivatives[J].J Math Anal Appl,2002,270(1):66-79.
[5]YANG Xiaojun.Advanced Local Fractional Calculus and Its Applications[M].New York:World Science Publisher,2012.
[6]GOLMANKHANEH A K,YANG Xiaojun,BALEANU D.Einstein Field Equations within Local Fractional Calculus[J].Roman J Phy,2015,60(2):22-31.
[7]MO Huixia,SUI Xin,YU Dongyan.Generalized Convex Functions on Fractal Sets and Two Related Inequalities[J/OL].Abstract Appl Anal,2014-06-15.http://dx.doi.org/10.1155/2014/636751.
[8]GRADSHTEYN I S,RYZHIK I M.Tables of Integrals,Series and Products[M].San Diego:Academic Press,2000.
[9]孙文兵.分形空间上的新Hadamard型不等式及应用[J].华东师范大学学报(自然科学版),2017(6):33-41.(SUN Wenbing.New Hadamard-Type Inequalities on Fractal Space and Their Applications[J].Journal of East China Normal University(Natural Science),2017(6):33-41.)