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

In this paper, we give and study the concept of n-polynomial (s,m)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(s,m)$\end{document}-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)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(s,m)$\end{document}-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)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(s,m)$\end{document}-exponential-type convex. Some applications to special means and new error estimates for the trapezoid formula are given.