Better approximations for quasi-convex functions

Huriye Kadakal

Abstract


In this paper, by using Hölder-İşcan, Hölder integral inequality and an general identity for differentiable functions we can get new estimates on generalization of Hadamard, Ostrowski and Simpson type integral inequalities for functions whose derivatives in absolute value at certain power are quasi-convex functions. It is proved that the result obtained Hölder-İşcan integral inequality is better than the result obtained Hölder inequality.


Keywords


Hölder-İşcan inequality; Hermite-Hadamard inequality; Simpson and Ostrowski type inequality; midpoint and trapezoid type inequality; quasi-convex functions.

Full Text:

PDF

References


S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.

S.S. Dragomir, J. Pecaric, and L.E. Persson, Some inequalities of Hadamard Type, Soochow Journal of Mathematics, 21(3) (1995), 335-341.

S.S. Dragomir and Th. M. Rassias, Ostrowski type inequalities and applications in numerical integration, Kluwer Academic Publishers, Dorcdrecht, Boston, London, 2002.

J. Hadamard, Etude sur les proprietes des fonctions entieres en particulier d'une fonction consideree par Riemann. J. Math. Pures Appl. 58 (1893), 171-215.

İ. İşcan, New Estimates on Generalization of Some Integral Inequalities for s-Convex Functions and Their Applications, International Journal of Pure and Applied Mathematics, 86(4) (2013), 727-746.

İ. İşcan, On generalization of some integral inequalities for quasi-convex functions and their applications, International Journal of Engineering and Applied Sciences, 3(1) (2013), 37-42.

İ. İşcan, New renements for integral and sum forms of Holder inequality, Journal of Inequalities and Applications. 2019(1) (2019), 1-11.

İ. İşcan, H. Kadakal and M. Kadakal, Some new integral inequalities for n-times differentiable quasi-convex functions. Sigma. 35(3) (2017), 363-368.

H. Kadakal, Multiplicatively P-functions and some new inequalities. New Trends in Mathematical Sciences. 6(4) (2018), 111-118.

H. Kadakal, Hermite-Hadamard type inequalities for trigonometrically convex functions, University of Bacau Faculty of Sciences Scientic Studies and Research Series Mathematics and Informatics. 28(2) (2019), 19-28.

H. Kadakal, New Inequalities for Strongly r-Convex Functions. Journal of Function Spaces. 2019 (2019), ID 1219237:10 pages.

M. Kadakal, İ. İşcan, P. Agarwal and M. Jleli, Exponential trigonometric convex functions and Hermite-Hadamard type inequalities. Mathematica Slovaca. 71(1) (2021), 43-56.

M. Kadakal, İ. İşcan, H. Kadakal and K. Bekar, On improvements of some integral inequalities, Honam Mathematical Journal. 43(3) (2021), 441-452.

M. Kadakal, H. Kadakal and İ. İşcan, Some new integral inequalities for n-times dierentiable s-convex functions in the first sense. Turkish Journal of Analysis and Number Theory. 5(2) (2017), 63-68.

H. Kadakal, M. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable s-convex and s-concave functions in the second sense. Mathematics and Statistic. 5(2) (2017), 94-98.

H. Kadakal, M. Kadakal and _I. _ Iscan, New type integral inequalities for three times differentiable preinvex and prequasiinvex functions. Open J. Math. Anal. 2(1) (2018), 33-46.

S. Maden, H. Kadakal, M. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable convex and concave functions. Journal of Nonlinear Sciences and Applications. 10(12) (2017), 6141-6148.

S. Ozcan, Some Integral Inequalities for Harmonically (; s)-Convex Functions. Journal of Function Spaces. 2019 (2019), Article ID 2394021, 8 pages.

S. Ozcan, İ. İşcan, Some new Hermite-Hadamard type inequalities for s-convex functions and their applications. Journal of Inequalities and Applications. 2009 (2019), 201.

M.Z. Sarikaya and N. Aktan, On the generalization of some integral inequalities and their applications, Mathematical and Computer Modelling, 54 (2011), 2175-2182.

M.Z. Sarikaya, E. Set and M.E. Ozdemir, On new inequalities of Simpson's type for convex functions, RGMIA Res. Rep. Coll. 13(2) (2010), Article 2.




DOI: http://dx.doi.org/10.24193/subbmath.2024.2.02

Refbacks

  • There are currently no refbacks.