Hermite-Jensen-Mercer-Type Inequalities via Caputo-Fabrizio Fractional Integral for h-Convex Function

被引：16
作者：
Vivas-Cortez, Miguel [1 ]
Saleem, Muhammad Shoaib [2 ]
Sajid, Sana [2 ]
Zahoor, Muhammad Sajid [2 ]
Kashuri, Artion [3 ]
机构：
[1] Pontificia Univ Catolica Ecuador, Sch Phys & Math Sci, Fac Exact & Nat Sci, Ave 12 October 1076, Quito 17012184, Ecuador
[2] Univ Okara, Dept Math, Okara 56300, Pakistan
[3] Univ Ismail Qemali, Fac Tech Sci, Dept Math, Vlore 9401, Albania
来源：
FRACTAL AND FRACTIONAL | 2021年 / 5卷 / 04期
关键词：
convex function; h-convex function; Hermite-Hadamard inequality; Caputo-Fabrizio fractional integral; Jensen inequality; Jensen-Mercer inequality; HADAMARD; VARIANT;
D O I：
10.3390/fractalfract5040269
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Integral inequalities involving many fractional integral operators are used to solve various fractional differential equations. In the present paper, we will generalize the Hermite-Jensen-Mercer-type inequalities for an h-convex function via a Caputo-Fabrizio fractional integral. We develop some novel Caputo-Fabrizio fractional integral inequalities. We also present Caputo-Fabrizio fractional integral identities for differentiable mapping, and these will be used to give estimates for some fractional Hermite-Jensen-Mercer-type inequalities. Some familiar results are recaptured as special cases of our results.
引用
收藏
页数：17
相关论文
共 46 条
  • [1] Fractional operators with exponential kernels and a Lyapunov type inequality
    Abdeljawad, Thabet
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2017,
  • [2] ON FRACTIONAL DERIVATIVES WITH EXPONENTIAL KERNEL AND THEIR DISCRETE VERSIONS
    Abdeljawad, Thabet
    Baleanu, Dumitru
    [J]. REPORTS ON MATHEMATICAL PHYSICS, 2017, 80 (01) : 11 - 27
  • [3] Some New Refinements of Hermite-Hadamard-Type Inequalities Involving ψk-Riemann-Liouville Fractional Integrals and Applications
    Awan, Muhammad Uzair
    Talib, Sadia
    Chu Yu-Ming
    Noor, Muhammad Aslam
    Noor, Khalida Inayat
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2020, 2020
  • [4] Baleanu D., 2016, FRACTIONAL CALCULUS
  • [5] 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
  • [6] SOME HERMITE-JENSEN-MERCER LIKE INEQUALITIES FOR CONVEX FUNCTIONS THROUGH A CERTAIN GENERALIZED FRACTIONAL INTEGRALS AND RELATED RESULTS
    Butt, Saad Ihsan
    Akdemir, Ahmet Ocak
    Nasir, Jamshed
    Jarad, Fahd
    [J]. MISKOLC MATHEMATICAL NOTES, 2020, 21 (02) : 689 - 715
  • [7] New Hermite-Jensen-Mercer-type inequalities via k-fractional integrals
    Butt, Saad Ihsan
    Umar, Muhammad
    Rashid, Saima
    Akdemir, Ahmet Ocak
    Chu, Yu-Ming
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [8] Hermite-Jensen-Mercer type inequalities for conformable integrals and related results
    Butt, Saad Ihsan
    Nadeem, Mehroz
    Qaisar, Shahid
    Akdemir, Ahmet Ocak
    Abdeljawad, Thabet
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [9] New fractional estimates for Hermite-Hadamard-Mercer's type inequalities
    Chu, Hong-Hu
    Rashid, Saima
    Hammou, Zakia
    Chu, Yu-Ming
    [J]. ALEXANDRIA ENGINEERING JOURNAL, 2020, 59 (05) : 3079 - 3089
  • [10] Cortez M. J. V., 2017, Rev. MATUA, V4, P62
12345