基于单调函数的Hermite-Hadamard不等式的加细
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摘要
考虑满足x Hermite-Hadamard type inequalities has been established with the consideration of four points, i.e. x, y, y′, x′, which can satisfy x
引文
[1] 廖俊俊,吴洁.关于凸性的一些探讨[J].大学数学,2016,32(6):91-95.
[2] 时统业,李照顺,夏琦,等.与MH凸函数有关的积分不等式和单调函数[J].广东第二师范学院学报,2016,36(3):23-29.
[3] 刘三阳,李广民.数学分析十讲[M].北京:科学出版社,2011.
[4] 裴礼文.数学分析中的典型问题与方法[M].2版.北京:高等教育出版社,2006.
[5] 张亚楠,刘长剑.关于凸函数单侧导数的连续性[J].大学数学,2015,31(4):53-54.
[6] 唐忠华,王传卫,朱根林,等.关于凸函数的一个分析性质的充要条件[J].大学数学,2009,25(4):174-176.
[7] 蒲义书,陈露.凸函数概述[J].高等数学研究,2006,9(4):34-36,71.
[8] 李微微,范胜君.凸函数的几何特征与分类[J].高等数学研究,2014,17(1):83-85.
[9] 刘文武.凸函数的一个等价性质[J].高等数学研究,2010,13(1):9-10.
[10] 何敏藩.胡诗国.凹凸函数的两个定义的等价性证明及应用[J].广东第二师范学院学报,2017,37(3):50-53.
[11] DRAGOMIR S S,PEARCE C E M.Selected topics on Hermite-Hadamard inequalities and applications[D].Victoria:Victoria University,2000.
[12] DRAGOMIR S S.Two mappings in connection to Hadamard’s inequalities[J].Journal of Mathematical Analysis and Applications,1992,167(1):49-56.
[13] DRAGOMIR S S.Further proprtities of some mapping associoateed with Hermite-Hadamard inequalities[J].Tamkang J Math,2003,34 (1):45-57.
[14] DRAGOMIR S S,MILO?EVI.On some refinements of Hadamard’s inequalities and applications[J].Publikacije Elektrotehnikog Fakulteta Serija Matematika,1993,4(2):3-10.
[15] TSENG K L,HWANG S R,DRAGOMIR S S.New Hermite-Hadamard-type inequalities for convex functions (II)[J].Computers and Mathematics with Applications,2011,62(1):401-418.
[16] TSENG K L,HWANG S R,DRAGOMIR S S.New Hermite-Hadamard-type inequalities for convex functions (I)[J].Applied Mathematics Letters,2012,25(6):1005-1009.
[17] DRAGOMIR S S,AGARWAL R P.Two new mappings associated with Hadamard’s inequalities for convex functions[J].Applied Mathematics Letters,1998,11(3):33-38.
[18] WANG L C.Some refinements of Hermite-Hadamard inequalities for convex functions[J].Publikacije Elektrotehnikog Fakulteta Serija Matematika,2004 (15):39-44.
[19] HWANG D Y,TSENG K L,YANG G S.Some Hadamard’s inequalities for co-ordinated convex functions in a rectangle from the plane[J].Taiwanese Journal of Mathematics,2007,11(1):63-73.
[20] MINCULETE N,MITROI F C.Fejer-type inequalities[J].Australian Journal of Mathematical Analysis and Applications,2011,9(1):1-8.
[21] 匡继昌.常用不等式[M].4版.济南:山东科学技术出版社,2010:430-436.
[22] 王良成.凸函数的Hadamard不等式的若干推广[J].数学的实践与认识,2002,32(6):1027-1030.
[23] 柯源,杨斌,胡明旸.Hermite-Hadamard不等式的推广[J].数学的实践与认识,2007,37(23):161-164.
[24] 时统业,李军.基于凸函数积分性质的Hermite-Hadamard不等式的加细[J].广东第二师范学院学报,2017,37(5):23-27.
[25] 时统业.涉及可微(α,m)凸函数的单调函数和Hermite-Hadamard型不等式[J].广东第二师范学院学报,2018,38(3):32-37.
[26] 李丹衡,邓远北.函数的左、右导数的应用[J].高等数学研究,1999,2(3):26-28.
[2] 时统业,李照顺,夏琦,等.与MH凸函数有关的积分不等式和单调函数[J].广东第二师范学院学报,2016,36(3):23-29.
[3] 刘三阳,李广民.数学分析十讲[M].北京:科学出版社,2011.
[4] 裴礼文.数学分析中的典型问题与方法[M].2版.北京:高等教育出版社,2006.
[5] 张亚楠,刘长剑.关于凸函数单侧导数的连续性[J].大学数学,2015,31(4):53-54.
[6] 唐忠华,王传卫,朱根林,等.关于凸函数的一个分析性质的充要条件[J].大学数学,2009,25(4):174-176.
[7] 蒲义书,陈露.凸函数概述[J].高等数学研究,2006,9(4):34-36,71.
[8] 李微微,范胜君.凸函数的几何特征与分类[J].高等数学研究,2014,17(1):83-85.
[9] 刘文武.凸函数的一个等价性质[J].高等数学研究,2010,13(1):9-10.
[10] 何敏藩.胡诗国.凹凸函数的两个定义的等价性证明及应用[J].广东第二师范学院学报,2017,37(3):50-53.
[11] DRAGOMIR S S,PEARCE C E M.Selected topics on Hermite-Hadamard inequalities and applications[D].Victoria:Victoria University,2000.
[12] DRAGOMIR S S.Two mappings in connection to Hadamard’s inequalities[J].Journal of Mathematical Analysis and Applications,1992,167(1):49-56.
[13] DRAGOMIR S S.Further proprtities of some mapping associoateed with Hermite-Hadamard inequalities[J].Tamkang J Math,2003,34 (1):45-57.
[14] DRAGOMIR S S,MILO?EVI.On some refinements of Hadamard’s inequalities and applications[J].Publikacije Elektrotehnikog Fakulteta Serija Matematika,1993,4(2):3-10.
[15] TSENG K L,HWANG S R,DRAGOMIR S S.New Hermite-Hadamard-type inequalities for convex functions (II)[J].Computers and Mathematics with Applications,2011,62(1):401-418.
[16] TSENG K L,HWANG S R,DRAGOMIR S S.New Hermite-Hadamard-type inequalities for convex functions (I)[J].Applied Mathematics Letters,2012,25(6):1005-1009.
[17] DRAGOMIR S S,AGARWAL R P.Two new mappings associated with Hadamard’s inequalities for convex functions[J].Applied Mathematics Letters,1998,11(3):33-38.
[18] WANG L C.Some refinements of Hermite-Hadamard inequalities for convex functions[J].Publikacije Elektrotehnikog Fakulteta Serija Matematika,2004 (15):39-44.
[19] HWANG D Y,TSENG K L,YANG G S.Some Hadamard’s inequalities for co-ordinated convex functions in a rectangle from the plane[J].Taiwanese Journal of Mathematics,2007,11(1):63-73.
[20] MINCULETE N,MITROI F C.Fejer-type inequalities[J].Australian Journal of Mathematical Analysis and Applications,2011,9(1):1-8.
[21] 匡继昌.常用不等式[M].4版.济南:山东科学技术出版社,2010:430-436.
[22] 王良成.凸函数的Hadamard不等式的若干推广[J].数学的实践与认识,2002,32(6):1027-1030.
[23] 柯源,杨斌,胡明旸.Hermite-Hadamard不等式的推广[J].数学的实践与认识,2007,37(23):161-164.
[24] 时统业,李军.基于凸函数积分性质的Hermite-Hadamard不等式的加细[J].广东第二师范学院学报,2017,37(5):23-27.
[25] 时统业.涉及可微(α,m)凸函数的单调函数和Hermite-Hadamard型不等式[J].广东第二师范学院学报,2018,38(3):32-37.
[26] 李丹衡,邓远北.函数的左、右导数的应用[J].高等数学研究,1999,2(3):26-28.