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

被引：104

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

页码：378 / 390

页数：13

共 32 条

[1] Magnetoelectronic properties of ferromagnetic compounds Rb2TaZ6(Z = Cl, Br) for possible spintronic applications
Ali, Malak Azmat
Murtaza, G.
Khan, Afzal
Algrafy, Eman
Mahmood, Asif
Ramay, Shahid M.
[J]. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, 2020, 120 (19)
[2] Nondifferentiable variational principles in terms of a quantum operator
Almeida, Ricardo
Torres, Delfim F. M.
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2011, 34 (18) : 2231 - 2241
[3] Alomari M., 2009, Research report collection, V12
[4] q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions
Alp, Necmettin
Sarikaya, Mehmet Zeki
Kunt, Mehmet
Iscan, Imdat
[J]. JOURNAL OF KING SAUD UNIVERSITY SCIENCE, 2018, 30 (02) : 193 - 203
[5] [Anonymous], 2000, HIST Q CALCULUS NEW
[6] [Anonymous], 2018, J DIABETES RES, DOI DOI 10.1016/j.patrec.2018.02.001
[7] ASKEY R, 1985, MEM AM MATH SOC, V54, P1
[8] On q-Hermite-Hadamard inequalities for general convex functions
Bermudo, S.
Korus, P.
Napoles Valdes, J. E.
[J]. ACTA MATHEMATICA HUNGARICA, 2020, 162 (01) : 364 - 374
[9] BRITO A. F. S., 2012, THESIS
[10] Cresson J, 2009, TOPOL METHOD NONL AN, V33, P217

← 1 2 3 4 →