2类凸函数的Hermite-Hadamard-Fejér型不等式
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摘要
介绍了一种已有的建立第1个Hermite-Hadamard-Fejér型不等式的方法,并以建立GA-凸函数的第1个Hermite-Hadamard型不等式为例来说明这种方法.使用该方法建立了2类凸函数的第1个Hermite-Hadamard-Fejér型不等式,作为特例,得到η-凸函数和广义几何凸函数的第1个Hermite-Hadamard-Fejér型不等式.
This paper introduces a method to establish the first Hermite-Hadamard-Fejétype inequality,and illustrates this method by establishing the first Hermite-Hadamard type inequality of GA-convex functions.With this method,the first Hermite-Hadamard-Fejér type inequalities of two classes of convex functions are established.The first Hermite-Hadamard-Fejér type inequalities ofη-convex functions and generalized geometrically convex functions are also obtained as particular cases.
This paper introduces a method to establish the first Hermite-Hadamard-Fejétype inequality,and illustrates this method by establishing the first Hermite-Hadamard type inequality of GA-convex functions.With this method,the first Hermite-Hadamard-Fejér type inequalities of two classes of convex functions are established.The first Hermite-Hadamard-Fejér type inequalities ofη-convex functions and generalized geometrically convex functions are also obtained as particular cases.
引文
[1]DRAGOMIR SEVER S,PEARCE CHARLES E M.Selected Topics on Hermite-Hadamard Inequalities and Applications[D].Victoria:Victoria University,2000.
[2]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.
[3]匡继昌.凸函数理论的最新进展[J].广东第二师范学院学报,2018,38(3):14-24.
[4]张小明,褚玉明.解析不等式新论[M].哈尔滨:哈尔滨工业大学出版社,2009:139-148;180-184;198-215.
[5]BOMBARDELLI MEA,VAROANEC SANJA.Properties of h-Convex Functions Related to the Hermite-HadamardFejér Inequalities[J].Computers and Mathematics with Applications,2009,58(9):1 869-1 877.
[6]DRAGOMIR SEVER S,FITZPATRICK SIMON.The Hadamard Inequalities for s-Convex Functions in the Second Sense[J].Demonstratio Mathematica,1999,32(4):687-696.
[7]GORDJI M ESHAGHI,DELAVAR M ROSTAMIAN,SEN M DE LA.Onφ-Convex Functions[J].Journal of Mathematical Inequalities,2016,10(1):173-183.
[8]NOOR MUHAMMAD ASLAM,NOOR KHALIDA INAYAT,SAFDAR FARHAT.Generalized Geometrically Convex Functions and Inequalities[J].Journal of Inequalities and Applications,2017,2017(1):202-220.
[9]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):1 027-1 030.
[10]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.
[11]华云.关于GA-凸函数的Hadamard型不等式[J].大学数学,2008,24(2):147-149.
[12]黄金莹,赵宇.广义凸函数的Hadamard不等式[J].重庆师范大学学报(自然科学版),2013,30(4):1-5.
[13]曾志红,时统业,钟建华,等.对称凸函数和弱对称凸函数的Hermite-Hadamard型不等式[J].西南师范大学学报(自然科学版),2018,43(4):24-30.
[14]VAROANEC SANJA.On h-Convexity[J].Journal of Mathematical Analysis and Applications,2007,326(1):303-311.
[2]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.
[3]匡继昌.凸函数理论的最新进展[J].广东第二师范学院学报,2018,38(3):14-24.
[4]张小明,褚玉明.解析不等式新论[M].哈尔滨:哈尔滨工业大学出版社,2009:139-148;180-184;198-215.
[5]BOMBARDELLI MEA,VAROANEC SANJA.Properties of h-Convex Functions Related to the Hermite-HadamardFejér Inequalities[J].Computers and Mathematics with Applications,2009,58(9):1 869-1 877.
[6]DRAGOMIR SEVER S,FITZPATRICK SIMON.The Hadamard Inequalities for s-Convex Functions in the Second Sense[J].Demonstratio Mathematica,1999,32(4):687-696.
[7]GORDJI M ESHAGHI,DELAVAR M ROSTAMIAN,SEN M DE LA.Onφ-Convex Functions[J].Journal of Mathematical Inequalities,2016,10(1):173-183.
[8]NOOR MUHAMMAD ASLAM,NOOR KHALIDA INAYAT,SAFDAR FARHAT.Generalized Geometrically Convex Functions and Inequalities[J].Journal of Inequalities and Applications,2017,2017(1):202-220.
[9]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):1 027-1 030.
[10]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.
[11]华云.关于GA-凸函数的Hadamard型不等式[J].大学数学,2008,24(2):147-149.
[12]黄金莹,赵宇.广义凸函数的Hadamard不等式[J].重庆师范大学学报(自然科学版),2013,30(4):1-5.
[13]曾志红,时统业,钟建华,等.对称凸函数和弱对称凸函数的Hermite-Hadamard型不等式[J].西南师范大学学报(自然科学版),2018,43(4):24-30.
[14]VAROANEC SANJA.On h-Convexity[J].Journal of Mathematical Analysis and Applications,2007,326(1):303-311.