Hermite–Hadamard-type inequalities via n -polynomial exponential-type convexity and their applications

Advances in Difference Equations

article

Butt, Saad Ihsan¹  Kashuri, Artion²  Tariq, Muhammad¹  Nasir, Jamshed³  Aslam, Adnan⁴  Gao, Wei⁵ 

[1] Department of Mathematics, COMSATS University Islamabad, Lahore Campus;Department of Mathematics, Faculty of Technical Science, University “Ismail Qemali”;Virtual University of Pakistan, Lahore Campus;Department of Natural Sciences and Humanities, University of Engineering and Technology;School of Information Science and Technology, Yunnan Normal University

关键词: Hermite–Hadamard inequality;    Hölder inequality;    Power mean inequality;    \((s;    m)\) -exponential-type convexity;    n -polynomial;   

DOI  :  10.1186/s13662-020-02967-5

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we give and study the concept of n-polynomial$(s,m)$ -exponential-type convex functions and some of their algebraic properties. We prove new generalization of Hermite–Hadamard-type inequality for the n-polynomial$(s,m)$ -exponential-type convex function ψ. We also obtain some refinements of the Hermite–Hadamard inequality for functions whose first derivatives in absolute value at certain power are n-polynomial$(s,m)$ -exponential-type convex. Some applications to special means and new error estimates for the trapezoid formula are given.

【 授权许可】

CC BY