Simpson and Newton type inequalities for convex functions via newly defined quantum integrals

被引：103
|
作者：
Budak, Huseyin [1 ]
Erden, Samet [2 ]
Ali, Muhammad Aamir [3 ]
机构：
[1] Duzce Univ, Fac Sci & Arts, Dept Math, Duzce, Turkey
[2] Bartin Univ, Fac Sci, Dept Math, Bartin, Turkey
[3] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2021年 / 44卷 / 01期
关键词：
convex function; quantum derivatives; quantum integral inequalities; Simpson inequality; HERMITE-HADAMARD INEQUALITIES;
D O I：
10.1002/mma.6742
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3 formula for convex mappings are provided. In addition, Newton type inequalities, for functions whose quantum derivatives in modulus or their powers are convex, are deduced. We also mention that the results in this work generalize inequalities given in earlier study.
引用
收藏
页码：378 / 390
页数：13
相关论文
共 50 条
  • [1] Simpson's and Newton's Type Inequalities for (α, m)-Convex Functions via Quantum Calculus
    Soontharanon, Jarunee
    Ali, Muhammad Aamir
    Budak, Huseyin
    Nonlaopon, Kamsing
    Abdullah, Zoya
    SYMMETRY-BASEL, 2022, 14 (04):
  • [2] ON INEQUALITIES OF SIMPSON?S TYPE FOR CONVEX FUNCTIONS VIA GENERALIZED FRACTIONAL INTEGRALS
    Kara, Hasan
    Budak, Huseyin
    Ali, Muhammad Aamir
    Hezenci, Fatih
    COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2022, 71 (03): : 806 - 825
  • [3] Simpson Type Integral Inequalities for Convex Functions via Riemann-Liouville Integrals
    Set, Erhan
    Akdemir, Ahmet Ocak
    Ozdemir, M. Emin
    FILOMAT, 2017, 31 (14) : 4415 - 4420
  • [4] On parameterized inequalities of Ostrowski and Simpson type for convex functions via generalized fractional integrals
    Budak, Huseyin
    Hezenci, Fatih
    Kara, Hasan
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (17) : 12522 - 12536
  • [5] SIMPSON TYPE QUANTUM INTEGRAL INEQUALITIES FOR CONVEX FUNCTIONS
    Tunc, M.
    Gov, E.
    Balgecti, S.
    MISKOLC MATHEMATICAL NOTES, 2018, 19 (01) : 649 - 664
  • [6] A new extension of quantum Simpson's and quantum Newton's type inequalities for quantum differentiable convex functions
    Ali, Muhammad Aamir
    Budak, Huseyin
    Zhang, Zhiyue
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (04) : 1845 - 1863
  • [7] Simpson- and Newton-Type Inequalities for Convex Functions via (p,q)-Calculus
    Luangboon, Waewta
    Nonlaopon, Kamsing
    Tariboon, Jessada
    Ntouyas, Sotiris K.
    MATHEMATICS, 2021, 9 (12)
  • [8] On inequalities of Simpson type for co-ordinated convex functions via generalized fractional integrals
    Kara, Hasan
    Budak, Huseyin
    Ali, Muhammad Aamir
    FILOMAT, 2023, 37 (08) : 2605 - 2631
  • [9] SIMPSON'S TYPE INEQUALITIES VIA THE KATUGAMPOLA FRACTIONAL INTEGRALS FOR s-CONVEX FUNCTIONS
    Kermausuor, Seth
    KRAGUJEVAC JOURNAL OF MATHEMATICS, 2021, 45 (05): : 709 - 720
  • [10] NEWTON-TYPE INEQUALITIES ASSOCIATED WITH CONVEX FUNCTIONS VIA QUANTUM CALCULUS
    Luangboon, Waewta
    Nonlaopon, Kamsing
    Sarikaya, Mehmet Zeki
    Budak, Huseyin
    MISKOLC MATHEMATICAL NOTES, 2024, 25 (01) : 383 - 398
12345