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SIMPSON TYPE INEQUALITIES FOR $Q-$CLASS FUNCTIONS\\[0pt]
\hrule

M. E. \"{O}zdemir$^{1}$, A. Ekinci$^{2},$ \textbf{M.G\"{u}rb\"{u}z}$^{2}$
and A. O. Akdemir$^{2}$

$^{1}$Department of Mathematics, Atat\"{u}rk University, Erzurum, Turkey $%
^{2}$Department of Mathematics , A\u{g}r\i\ \.{I}brahim \c{C}e\c{c}en
University, A\u{g}r\i , Turkey
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\textbf{Abstract}

In this paper, we obtain some Simpson type inequalities for functions whose
second derivatives' absolute value or q-th power of them are $Q-$class
functions. Also we give applications to numerical integration.

\textbf{References}

[1] M. Alomari, M. Darus and S.S. Dragomir, New inequalities of Simpson's
type for $s-$convex functions with applications, RGMIA Res. Rep. Coll., 12
(4) (2009).

[2] M. Alomari and M. Darus, On some inequalities of Simpson-type via
quasi-convex functions and applications,\ Transylvanian Journal of
Mathematics and Mechanics, vol. 2, no. 1, pp. 15--24, 2010.

[3] M.Z. Sarikaya, E. Set and M.E. \"{O}zdemir, On new inequalities of
Simpson's type for $s-$convex functions, Comput. Math. Appl. 60 (2010)
2191--2199.

[4] S. S. Dragomir, R. P. Agarwal, and P. Cerone, On Simpson's inequality
and applications, Journal of Inequalities and Applications, vol. 5, no. 6,
pp. 533--579, 2000.

[5] N.Ujevi\'{c}, Sharp inequalities of Simpson type and Ostrowski type,
Comp. Math. Appl., 48 (2004), 145-151.

[6] N.Ujevi\'{c}, Two sharp inequalities of Simpson type and applications,
Georgian Math. J., 1 (11) (2004), 187--194.

[7] E.K. Godunova, V.I. Levin, Neravenstva dlja funkcii \v{s}irokogo klassa,
soder\v{z}a\v{s}cego vypuklye, monotonnye i nekotorye drugie vidy funkcii,
in: Vycislitel. Mat. i. Mat. Fiz. Me\v{z}vuzov. Sb. Nauc. Trudov, MGPI,
Moskva, 1985, 138--142.

[8] D.S. Mitrinovi\'{c}, J. Pe\v{c}ari\'{c} and A.M. Fink,\ Classical and
new inequalities in analysis, \textit{Kluwer Academic Publishers},
Dordrecht, 1993.\hrule

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