Some integral inequalities for s-convex functions
Abstract
In the paper, by virtue of an integral identity and the H\"older inequality for integrals, the authors establish some new inequalities of the Hermite--Hadamard type for $s$-convex functions, derives some new inequalities for common convex functions, and apply these new results to construct some inequalities for special means.
Keywords
References
- \begin{thebibliography}{99}
- \bibitem{1} R.-F. Bai, F. Qi, and B.-Y. Xi, \textit{Hermite-Hadamard type inequalities for the $m$- and $(\alpha,m)$-logarithmically convex functions}, Filomat \textbf{27} (2013), no.~1, 1\nobreakdash--7.
- \bibitem{2} S.-P. Bai, S.-H. Wang, and F. Qi, \textit{Some Hermite-Hadamard type inequalities for $n$-time differentiable $(\alpha,m)$-convex functions}, J. Inequal. Appl. 2012, \textbf{2012}:267, 11~pages; Available online at \url{https://doi.org/10.1186/1029-242X-2012-267}.
- \bibitem{3} L. Chun and F. Qi, \textit{Integral inequalities of Hermite-Hadamard type for functions whose third derivatives are convex}, J. Inequal. Appl. 2013, \textbf{2013}:451, 10~pages; Available online at \url{https://doi.org/10.1186/1029-242X-2013-451}.
- \bibitem{4} H. Hudzik and L. Maligranda, \emph{Some remarks on $s$-convex functions}, Aequationes Math. \textbf{48} (1994), no.~1, 100\nobreakdash--111; Available online at \url{https://doi.org/10.1007/BF01837981}.
- \bibitem{5} S. Hussain, M. I. Bhatti, and M. Iqbal, \emph{Hadamard-type inequalities for $s$-convex functions I}, Punjab Univ. J. Math. (Lahore) \textbf{41} (2009), 51\nobreakdash--60.
- \bibitem{6} U. S. Kirmaci, M. Klari\v{c}i\'c Bakula, M. E. \"{O}zdemir, and J. Pe\v{c}ari\'{c}, \emph{Hadamard-type inequalities for $s$-convex functions}, Appl. Math. Comput. \textbf{193} (2007), no.~1, 26\nobreakdash--35; Available online at \url{https://doi.org/10.1016/j.amc.2007.03.030}.
- \bibitem{7} F. Qi, Z.-L. Wei, and Q. Yang, \textit{Generalizations and refinements of Hermite-Hadamard's inequality}, Rocky Mountain J. Math. \textbf{35} (2005), no.~1, 235\nobreakdash--251; Available online at \url{https://doi.org/10.1216/rmjm/1181069779}.
Details
Primary Language
English
Subjects
Engineering
Journal Section
Research Article
Publication Date
December 1, 2018
Submission Date
November 27, 2017
Acceptance Date
July 5, 2018
Published in Issue
Year 2018 Volume: 31 Number: 4