Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

ON IMPROVEMENTS OF SOME INTEGRAL INEQUALITIES

  • Kadakal, Mahir (Department of Mathematics, Faculty of Arts and Sciences, Giresun University) ;
  • Iscan, Imdat (Department of Mathematics, Faculty of Arts and Sciences, Giresun University) ;
  • Kadakal, Huriye (Ministry of Education, Hamdi Bozbag Anatolian High School) ;
  • Bekar, Kerim (Department of Mathematics, Faculty of Arts and Sciences, Giresun University)
  • Received : 2021.03.06
  • Accepted : 2021.05.10
  • Published : 2021.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, improved power-mean integral inequality, which provides a better approach than power-mean integral inequality, is proved. Using Hölder-İşcan integral inequality and improved power-mean integral inequality, some inequalities of Hadamard's type for functions whose derivatives in absolute value at certain power are quasi-convex are given. In addition, the results obtained are compared with the previous ones. Then, it is shown that the results obtained together with identity are better than those previously obtained.

Keywords

References

  1. Alomari, M., Darus, M. and Kirmaci, US., Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Computers and Mathematics with Applications, 59 (2010) 225-232. https://doi.org/10.1016/j.camwa.2009.08.002
  2. Alomari, M., Darus, M. and Kirmaci, U.S., Some inequalities of Hermite-Hadamard type for s-convex functions, Acta Math. Scientia, vol. 31B, No 4, (2011), 1643-1652. https://doi.org/10.1016/S0252-9602(11)60350-0
  3. Dragomir, S.S. and Pearce, C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  4. Iscan, I., On generalization of some integral inequalities for quasi-convex and their applications, International Journal of Engineering and Applied Sciences, 3 (1) (2013), 37-42.
  5. Iscan, I., New refinements for integral and sum forms of Holder inequality, Journal of Inequalities and Applications, 2019.1 (2019): 1-11. https://doi.org/10.1186/s13660-019-1955-4
  6. Kirmaci, U.S., Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput. 147 (2004), 137-146. https://doi.org/10.1016/S0096-3003(02)00657-4
  7. D.S. Mitrinovic, J.E. Pecaric, and A.M. Fink. Classical and new inequalities in analysis, Kluwer Akademic Publishers, Dordrecht, Boston, London, 1993.