A new q-integral identity and estimation of its bounds involving generalized exponentially μ-preinvex functions

Advances in Difference Equations

Muhammad Aslam Noor¹  Khalida Inayat Noor¹  Artion Kashuri²  Muhammad Uzair Awan³  Sadia Talib³  Yu-Ming Chu⁴ 

[1] Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan;Department of Mathematics, Faculty of Technical Science, University “Ismail Qemali”, Vlora, Albania;Department of Mathematics, Government College University, Faisalabad, Pakistan;Department of Mathematics, Huzhou University, Huzhou, China;Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, China;

关键词: Hermite–Hadamard inequality;    Hölder inequality;    Power mean inequality;    Convexity;    μ;    Quantum calculus;    26A51;    26D15;    05A30;   

DOI  :  10.1186/s13662-020-03036-7

来源: Springer

【 摘 要 】

In the article, we introduce the generalized exponentially μ-preinvex function, derive a new q-integral identity for second order q-differentiable function, and establish several new q-trapezoidal type integral inequalities for the function whose absolute value of second q-derivative is exponentially μ-preinvex.

【 授权许可】

CC BY