Hermite-Hadamard-Fejer type inequalities involving generalized fractional integral operators

被引:3
作者
Set, Erhan [1 ]
Choi, Junesang [2 ]
Alan, E. Aykan [1 ]
机构
[1] Ordu Univ, Fac Sci & Arts, Dept Math, Ordu, Turkey
[2] Dongguk Univ, Dept Math, Gyeongju 38066, South Korea
关键词
Convex function; Quasi-convex function; Symmetrized convex function; Wright-quasi-convex functions; Hermite-Hadamard type inequalities; Generalized fractional integral operators; Hermite-Hadamard-Fejer type inequalities; 26A33; 26D10; 26D15; 33B20;
D O I
10.1007/s41478-018-0159-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Since the so-called Hermite-Hadamard type inequalities for convex functions were presented, their generalizations, refinements, and variants involving various integral operators have been extensively investigated. Here we aim to establish several Hermite-Hadamard-Fejer type inequalities for symmetrized convex functions and Wright-quasi-convex functions with a weighted function symmetric with respect to the midpoint axis on the interval involving the known generalized fractional integral operators. We also point out that certain known inequalities are particular cases of the results presented here.
引用
收藏
页码:1007 / 1027
页数:21
相关论文
共 29 条
  • [1] Agarwal R.P., 2016, Fasc. Math, V56, P5, DOI [10.1515/fascmath-2016-0001, DOI 10.1515/FASCMATH-2016-0001]
  • [2] Properties of h-convex functions related to the Hermite-Hadamard-Fejer inequalities
    Bombardelli, Mea
    Varosanec, Sanja
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (09) : 1869 - 1877
  • [3] Dahmani Z., 2010, INT J NONLIN SCI NUM, V9, P493
  • [4] Dragomir S., 2000, Selected Topics on Hermite-Hadamard Inequalities and Applications
  • [5] SYMMETRIZED CONVEXITY AND HERMITE-HADAMARD TYPE INEQUALITIES
    Dragomir, S. S.
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2016, 10 (04): : 901 - 918
  • [6] Dragomir S. S., 2017, RGMIA RES REP COLL, V20, P15
  • [7] Quasi-convex functions and Hadamard's inequality
    Dragomir, SS
    Pearce, CEM
    [J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1998, 57 (03) : 377 - 385
  • [8] El Farissi A, 2012, REAL ANAL EXCH, V38, P467
  • [9] Fejr L., 1906, Anz Ungar. Akad. Wiss., V24, P369
  • [10] Gorenflo R., 1997, FRACTIONAL CALCULUS, P223, DOI DOI 10.1007/978-3-7091-2664-6_5