Research Article

On new Simpson’s type ınequalities for trigonometrically convex functions with applications

Volume: 41 Number: 4 December 29, 2020
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On new Simpson’s type ınequalities for trigonometrically convex functions with applications

Abstract

The aim of this article is to define a special case of h- convex function, namely the notion of a trigonometrically convex function. Using the Hölder, Hölder-İşcan integral inequality and the power-mean, improved power-mean integral inequalities, and together with an integral identity, some new Simpson-type inequalities have been obtained for trigonometric convex functions. We also give some applications for special means.

Keywords

References

  1. [1] Dragomir S.S., Pearce C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  2. [2] Maden S., Kadakal H., Kadakal M. and İşcan İ., Some new integral inequalities for n-times differentiable convex and concave functions, Journal of Nonlinear Sciences and Applications, 10(12) (2017) 6141-6148.
  3. [3] Dragomir S.S., Agarwal R.P. and Cerone P., On Simpson’s inequality and applications, J. of Inequal. Appl., 5 (2000) 533-579.
  4. [4] İşcan İ., Bekar K. and Numan S., Hermite-Hadamard and Simpson type inequalities for differentiable quasi-geometrically convex functions, Turkish Journal of Analysis and Number Theory, 2 (2) (2014) 42-46.
  5. [5] Kadakal M., Kadakal H. and İşcan İ., Some new integral inequalities for n-times differentiable s-convex functions in the first sense, Turkish Journal of Analysis and Number Theory, 5(2) (2017) 63-68.
  6. [6] Set E., Ozdemir M.E. and Sarikaya M.Z., On new inequalities of Simpson’s type for quasi-convex functions with applications, Tamkang Journal of Mathematics, 43(3) (2012) 357–364.
  7. [7] Varosanec S., On h-convexity, J. Math. Anal. Appl., 326 (2007) 303-311.
  8. [8] Kadakal H., Hermite-Hadamard type inequalities for trigonometrically convex functions, Scientific Studies and Research. Series Mathematics and Informatics, 28 (2) (2018) 19-28.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Publication Date

December 29, 2020

Submission Date

June 9, 2020

Acceptance Date

September 18, 2020

Published in Issue

Year 2020 Volume: 41 Number: 4

DOI

https://doi.org/10.17776/csj.749571

IZ

https://izlik.org/JA32FM83FZ

Cite

RIS / Bibtex
APA
Demir, Ş., Maden, S., İşcan, İ., & Kadakal, M. (2020). On new Simpson’s type ınequalities for trigonometrically convex functions with applications. Cumhuriyet Science Journal, 41(4), 862-874. https://doi.org/10.17776/csj.749571

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