(α,m)凸函数的新的Hermite-Hadamard型不等式
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摘要
从(α,m)凸函数的定义出发,建立了(α,m)凸函数的Hermite-Hadamard型不等式,其中的一个不等式推广了已有文献关于第一种意义上的(α,m)凸函数的结果.
Starting from the definition of(α,m)-convex functions,Hermite-Hadamard type inequalities of(α,m)-convex function are established. One of the Hermite-Hadamard type inequalities extends the existing literature result about(α,m)-convex functions in the first sense.
Starting from the definition of(α,m)-convex functions,Hermite-Hadamard type inequalities of(α,m)-convex function are established. One of the Hermite-Hadamard type inequalities extends the existing literature result about(α,m)-convex functions in the first sense.
引文
[1]TOADER G H. Some generalizations of the convexity[M]//Proceedings of the colloquium on approximation and optimization. University of Cluj-Napoca,1984:329-338.
[2]DRAGOMIR S S,TOADER G H. Some inequalities for m-convex functions[J]. Studia Univ Babes-Bolyai Math,1993,38(1):21-28.
[3]HUDZIK H,MALIGRANDA L. Some remarks on s-convex functions[J]. Aequationes Mathematicae,1994,48(1):100-111.
[4]MIHESAN V G.A generalization of the convexity,seminar on functional equations,approx,convex[M].Romania:Cluj-Napoca,1993.
[5]PARK J. Some Hadamard's type inequalities for co-ordinated(s,m)-convex mappings in the second sense[J].Far East Journal of Mathematical Sciences,2011,2(2):205-216.
[6]BAKULA M K,PECARIC J,RIBICIC M. Companion inequalities to Jensen's inequality for m-convex and(α,m)-convex functions[J]. Journal of Inequalities in Pure and Applied Mathematics,2006,7(5):1-32.
[7]SET E,SARDARI M,ZDEMIR M E,et al. On generalizations of the Hadamard inequality for(α,m)-convex functions[J]. Kyungpook Mathematical Journal,2012,52(3):307-317.
[8]双叶,尹红萍.关于(α,m)凸函数的几个积分不等式及其应用[J].湖北民族学院学报(自然科学版),2017,35(3):292-296.
[9]BAKULA M K,ZDEMIR M E,PECARIC J. Hadamard type inequalities for m-convex and(α,m)-convex functions[J]. Journal of Inequalities in Pure and Applied Mathematics,2008,9(4):article 96.
[10]ZDEMIR M E,AVCI M,KAVURMACI H. Hermite-Hadamard-type inequalities via(α,m)-convexity[J].Computers and Mathematics with Applications,2011,61(9):2614-2620.
[11]SUN W N,LIU Q N. New Hermite-Hadamard type inequalities for(α,m)-convex functions and applications to special means[J]. Journal of Mathematical Inequalities,2017,11(2):383-397.
[12]李玉娇,杜廷松.一类(α,m)-凸函数的Hadamard型不等式[J].上海大学学报(自然科学版),2017,23(4):583-589.
[13]CORTEZ M V. Fejer type inequalities for(s,m)-convex functions in second sense[J]. Applied Mathematics and Information Sciences,2016,10(5):1-8.
[14]ZDEMIR M E,KAVURMACI H,SET E. Ostrowski's type inequalities for(α,m)-convex function[J].Kyungpook Mathematical Journal,2010,50(3):371-378.
[15]BAI S P,WANG S H,Qi F. Some Hermite-Hadamard type inequalities for n-time differentiable(α,m)-convex functions[J]. Journal of Inequalities and Applications,2012(1):267.
[16]IMDAT ICAN. A new generalization of some integral inequalities for(α,m)-convex functions[J]. Mathematical Sciences,2013,7(1):1-8.
[17]VIVAS M. Fejer type inequalities for(s,m)-convex functions in second sense[J]. Applied Mathematics and Information Sciences,2016,10(5):1-8.
[18]EU I,PARK J. On the simpson-like type inequalities for twice differentiable(α,m)-convex mappings[J].International Journal of Pure and Applied Mathematics,2012,78(5):617-634.
[19]WANG S H,Xi B Y,Qi F. On Hermite-Hadamard type inequalities for(α,m)-convex functions[J]. Int J Open Problems Comput Math,2012,5(4):46-57.
[20]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.
[21]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.
[2]DRAGOMIR S S,TOADER G H. Some inequalities for m-convex functions[J]. Studia Univ Babes-Bolyai Math,1993,38(1):21-28.
[3]HUDZIK H,MALIGRANDA L. Some remarks on s-convex functions[J]. Aequationes Mathematicae,1994,48(1):100-111.
[4]MIHESAN V G.A generalization of the convexity,seminar on functional equations,approx,convex[M].Romania:Cluj-Napoca,1993.
[5]PARK J. Some Hadamard's type inequalities for co-ordinated(s,m)-convex mappings in the second sense[J].Far East Journal of Mathematical Sciences,2011,2(2):205-216.
[6]BAKULA M K,PECARIC J,RIBICIC M. Companion inequalities to Jensen's inequality for m-convex and(α,m)-convex functions[J]. Journal of Inequalities in Pure and Applied Mathematics,2006,7(5):1-32.
[7]SET E,SARDARI M,ZDEMIR M E,et al. On generalizations of the Hadamard inequality for(α,m)-convex functions[J]. Kyungpook Mathematical Journal,2012,52(3):307-317.
[8]双叶,尹红萍.关于(α,m)凸函数的几个积分不等式及其应用[J].湖北民族学院学报(自然科学版),2017,35(3):292-296.
[9]BAKULA M K,ZDEMIR M E,PECARIC J. Hadamard type inequalities for m-convex and(α,m)-convex functions[J]. Journal of Inequalities in Pure and Applied Mathematics,2008,9(4):article 96.
[10]ZDEMIR M E,AVCI M,KAVURMACI H. Hermite-Hadamard-type inequalities via(α,m)-convexity[J].Computers and Mathematics with Applications,2011,61(9):2614-2620.
[11]SUN W N,LIU Q N. New Hermite-Hadamard type inequalities for(α,m)-convex functions and applications to special means[J]. Journal of Mathematical Inequalities,2017,11(2):383-397.
[12]李玉娇,杜廷松.一类(α,m)-凸函数的Hadamard型不等式[J].上海大学学报(自然科学版),2017,23(4):583-589.
[13]CORTEZ M V. Fejer type inequalities for(s,m)-convex functions in second sense[J]. Applied Mathematics and Information Sciences,2016,10(5):1-8.
[14]ZDEMIR M E,KAVURMACI H,SET E. Ostrowski's type inequalities for(α,m)-convex function[J].Kyungpook Mathematical Journal,2010,50(3):371-378.
[15]BAI S P,WANG S H,Qi F. Some Hermite-Hadamard type inequalities for n-time differentiable(α,m)-convex functions[J]. Journal of Inequalities and Applications,2012(1):267.
[16]IMDAT ICAN. A new generalization of some integral inequalities for(α,m)-convex functions[J]. Mathematical Sciences,2013,7(1):1-8.
[17]VIVAS M. Fejer type inequalities for(s,m)-convex functions in second sense[J]. Applied Mathematics and Information Sciences,2016,10(5):1-8.
[18]EU I,PARK J. On the simpson-like type inequalities for twice differentiable(α,m)-convex mappings[J].International Journal of Pure and Applied Mathematics,2012,78(5):617-634.
[19]WANG S H,Xi B Y,Qi F. On Hermite-Hadamard type inequalities for(α,m)-convex functions[J]. Int J Open Problems Comput Math,2012,5(4):46-57.
[20]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.
[21]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.