p,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( p,q\right) $$\end{document}-Hermite–Hadamard inequalities and p,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( p,q\right) $$\end{document}-estimates for midpoint type inequalities via convex and quasi-convex functions

被引:0
作者
Mehmet Kunt
İmdat İşcan
Necmettin Alp
Mehmet Zeki Sarıkaya
机构
[1] Karadeniz Technical University,Department of Mathematics, Faculty of Sciences
[2] Giresun University,Department of Mathematics, Faculty of Sciences and Arts
[3] Düzce University,Department of Mathematics, Faculty of Science and Arts
来源
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2018年 / 112卷 / 4期
关键词
Hermite–Hadamard inequality; Midpoint type inequality; -integral inequalities; -integral; -derivative; -integration; Convexity; Quasi-convexity; 34A08; 26A51; 26D15;
D O I
10.1007/s13398-017-0402-y
中图分类号
学科分类号
摘要
In this paper, we prove the correct p,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( p,q\right) $$\end{document}-Hermite–Hadamard inequality, some new p,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( p,q\right) $$\end{document}-Hermite–Hadamard inequalities, and generalized p,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( p,q\right) $$\end{document}-Hermite–Hadamard inequality. By using the left hand part of the correct p,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( p,q\right) $$\end{document}-Hermite–Hadamard inequality, we have a new equality. Finally using the new equality, we give some p,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( p,q\right) $$\end{document}-midpoint type integral inequalities through p,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( p,q\right) $$\end{document}-differentiable convex and p,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( p,q\right) $$\end{document}-differentiable quasi-convex functions. Many results given in this paper provide extensions of others given in previous works.
引用
收藏
页码:969 / 992
页数:23
相关论文
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