On Some New Inequalities of Hermite–Hadamard Midpoint and Trapezoid Type for Preinvex Functions in p,q-Calculus

Symmetry

Jarunee Soontharanon¹  Sotiris K. Ntouyas²  Ghulam Murtaza³  Muhammad Aamir Ali⁴  Thanin Sitthiwirattham⁵  Ifra Bashir Sial⁶ 

[1] Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand;Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece;Department of Mathematics, University of Management and Technology, Lahore 54700, Pakistan;Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China;Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand;School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China;

关键词: Hermite–Hadamard inequality;    (p,q)-integral;    post quantum calculus;    convex function;   

DOI  :  10.3390/sym13101864

来源: DOAJ

【 摘 要 】

In this paper, we establish some new Hermite–Hadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for $\left(p,q\right)$-differentiable preinvex functions in the context of $\left(p,q\right)$-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.

【 授权许可】

Unknown