Research Article
BibTex RIS Cite

Some integral inequalities for s-convex functions

Year 2018, Volume: 31 Issue: 4, 1192 - 1200, 01.12.2018

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.

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}.
  • \bibitem{8} M. Z. Sarikaya, E. Set, and M. E. \"Ozdemir, \emph{On new inequalities of Simpson's type for $s$-convex functions}, Comput. Math. Appl. \textbf{60} (2010), no.~8, 2191\nobreakdash--2199; Availble online at \url{https://doi.org/10.1016/j.camwa.2010.07.033}.
  • \bibitem{9} S.-H. Wang, B.-Y. Xi, and F. Qi, \textit{Some new inequalities of Hermite-Hadamard type for $n$-time differentiable functions which are $m$-convex}, Analysis (Munich) \textbf{32} (2012), no.~3, 247\nobreakdash--262; Available online at \url{https://doi.org/10.1524/anly.2012.1167}.
  • \bibitem{10} B.-Y. Xi and F. Qi, \textit{Some Hermite-Hadamard type inequalities for differentiable convex functions and applications}, Hacet. J. Math. Stat. \textbf{42} (2013), no.~3, 243\nobreakdash--257.
  • \end{thebibliography}
Year 2018, Volume: 31 Issue: 4, 1192 - 1200, 01.12.2018

Abstract

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}.
  • \bibitem{8} M. Z. Sarikaya, E. Set, and M. E. \"Ozdemir, \emph{On new inequalities of Simpson's type for $s$-convex functions}, Comput. Math. Appl. \textbf{60} (2010), no.~8, 2191\nobreakdash--2199; Availble online at \url{https://doi.org/10.1016/j.camwa.2010.07.033}.
  • \bibitem{9} S.-H. Wang, B.-Y. Xi, and F. Qi, \textit{Some new inequalities of Hermite-Hadamard type for $n$-time differentiable functions which are $m$-convex}, Analysis (Munich) \textbf{32} (2012), no.~3, 247\nobreakdash--262; Available online at \url{https://doi.org/10.1524/anly.2012.1167}.
  • \bibitem{10} B.-Y. Xi and F. Qi, \textit{Some Hermite-Hadamard type inequalities for differentiable convex functions and applications}, Hacet. J. Math. Stat. \textbf{42} (2013), no.~3, 243\nobreakdash--257.
  • \end{thebibliography}
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Ye Shuang This is me

Feng Qı 0000-0001-6239-2968

Publication Date December 1, 2018
Published in Issue Year 2018 Volume: 31 Issue: 4

Cite

APA Shuang, Y., & Qı, F. (2018). Some integral inequalities for s-convex functions. Gazi University Journal of Science, 31(4), 1192-1200.
AMA Shuang Y, Qı F. Some integral inequalities for s-convex functions. Gazi University Journal of Science. December 2018;31(4):1192-1200.
Chicago Shuang, Ye, and Feng Qı. “Some Integral Inequalities for S-Convex Functions”. Gazi University Journal of Science 31, no. 4 (December 2018): 1192-1200.
EndNote Shuang Y, Qı F (December 1, 2018) Some integral inequalities for s-convex functions. Gazi University Journal of Science 31 4 1192–1200.
IEEE Y. Shuang and F. Qı, “Some integral inequalities for s-convex functions”, Gazi University Journal of Science, vol. 31, no. 4, pp. 1192–1200, 2018.
ISNAD Shuang, Ye - Qı, Feng. “Some Integral Inequalities for S-Convex Functions”. Gazi University Journal of Science 31/4 (December 2018), 1192-1200.
JAMA Shuang Y, Qı F. Some integral inequalities for s-convex functions. Gazi University Journal of Science. 2018;31:1192–1200.
MLA Shuang, Ye and Feng Qı. “Some Integral Inequalities for S-Convex Functions”. Gazi University Journal of Science, vol. 31, no. 4, 2018, pp. 1192-00.
Vancouver Shuang Y, Qı F. Some integral inequalities for s-convex functions. Gazi University Journal of Science. 2018;31(4):1192-200.