TY  - JOUR
T1  - Generalized Simpson Type Integral Inequalities
AU  - Sarıkaya, Mehmet Zeki
AU  - Bardak, Sakine
PY  - 2019
DA  - April
Y2  - 2019
JF  - Konuralp Journal of Mathematics
JO  - Konuralp J. Math.
PB  - Mehmet Zeki SARIKAYA
WT  - DergiPark
SN  - 2147-625X
SP  - 186
EP  - 191
VL  - 7
IS  - 1
LA  - en
AB  - In this paper, we have established some generalized Simpson type inequalities for convex functions. Furthermore, inequalities obtained in special case present a refinement and improvement of previously known results.
KW  - Simpson type inequalities
KW  - convex functions
KW  - integral inequalities
CR  - [1] M. Alomari, M. Darus and S.S. Dragomir, New inequalities of Simpson´ıs type for sconvex functions with applications, RGMIA Res. Rep. Coll., 12 (4)
(2009), Article 9.
CR  - [2] S.S. Dragomir, R.P. Agarwal and P. Cerone, On Simpson´ıs inequality and applications, J. of Inequal. Appl., 5(2000), 533-579.
CR  - [3] S.S. Dragomir. On Simpson’s quadrature formula for differentiable mappings whose derivatives belong to lp spaces and applications. J. KSIAM, 2
(1998), 57–65.
CR  - [4] S.S. Dragomir, On Simpson’s quadrature formula for Lipschitzian mappings and applications Soochow J. Mathematics, 25 (1999), 175–180.
CR  - [5] T. Du, Y. Li and Z. Yang, A generalization of Simpson’s inequality via differentiable mapping using extended (s;m)-convex functions, Applied
Mathematics and Computation 293 (2017) 358–369
CR  - [6] S. Hussain and S. Qaisar, More results on Simpson’s type inequality through convexity for twice differentiable continuous mappings. Springer Plus
(2016), 5:77.
CR  - [7] B.Z. Liu, An inequality of Simpson type, Proc. R. Soc. A, 461 (2005), 2155-2158.
CR  - [8] J. Pecaric, F. Proschan and Y.L. Tong, Convex functions, partial ordering and statistical applications, Academic Press, New York, 1991.
CR  - [9] J. Pecaric., and S. Varosanec, A note on Simpson’s inequality for functions of bounded variation, Tamkang Journal of Mathematics, Volume 31, Number
3, Autumn (2000), 239–242.
CR  - [10] S. Qaisar, C.J. He, S. Hussain, A generalizations of Simpson’s type inequality for differentiable functions using (a;m)-convex functions and applications,
J. Inequal. Appl. 2013 (2013) 13. Article 158.
CR  - [11] H. Kavurmaci, A. O. Akdemir, E. Set and M. Z. Sarikaya, Simpson’s type inequalities for m􀀀 and (a;m)-geometrically convex functions, Konuralp
Journal of Mathematics, 2(1), pp:90-101, 2014.
CR  - [12] M. E. Ozdemir, A. O. Akdemir and H. Kavurmacı, On the Simpson’s inequality for convex functions on the co-Ordinates, Turkish Journal of Analysis
and Number Theory. 2014, 2(5), 165-169.
CR  - [13] M. Z. Sarikaya, E. Set and M. E. Ozdemir, On new inequalities of Simpson’s type for s-convex functions, Computers and Mathematics with Applications
60 (2010) 2191–2199.
CR  - [14] M.Z. Sarikaya, E. Set, M.E. Ozdemir, On new inequalities of Simpson’s type for convex functions, RGMIA Res. Rep. Coll. 13 (2) (2010) Article2.
CR  - [15] M. Z.Sarikaya, E. Set and M. E. Ozdemir, On new inequalities of Simpson’s type for functions whose second derivatives absolute values are convex,
Journal of Applied Mathematics, Statistics and Informatics , 9 (2013), No. 1.
CR  - [16] M.Z. Sarıkaya, T. Tunc and H. Budak, Simpson’s type inequality for F-convex function, Facta Universitatis Ser. Math. Inform., Vol. 32, No 5 (2017),
747–753.
CR  - [17] E. Set, M. E. Ozdemir and M. Z. Sarikaya, On new inequalities of Simpson’s type for quasi-convex functions with applications, Tamkang Journal of
Mathematics, 43 (2012), no. 3, 357–364.
CR  - [18] E. Set, M. Z. Sarikaya and N. Uygun, On new inequalities of Simpson’s type for generalized quasi-convex functions, Advances in Inequalities and
Applications, 2017, 2017:3, pp:1-11.
CR  - [19] K. L. Tseng, G. S. Yang and S.S. Dragomir, On weighted Simpson type inequalities and applications Journal of mathematical inequalities, Vol. 1,
number 1 (2007), 13–22.
CR  - [20] N. Ujevic, Double integral inequalities of Simpson type and applications, J. Appl. Math. Comput., 14 (2004), no:1-2, p. 213-223.
CR  - [21] Z.Q. Yang, Y.J. Li andT. Du, A generalization of Simpson type inequality via differentiable functions using (s;m)-convex functions, Ital. J. Pure Appl.
Math. 35 (2015) 327–338.
UR  - https://dergipark.org.tr/en/pub/konuralpjournalmath/issue//539070
L1  - https://dergipark.org.tr/en/download/article-file/699894
ER  -