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Year 2019, Volume: 7 Issue: 1, 186 - 191, 15.04.2019

Mehmet Zeki Sarıkaya Sakine Bardak

Abstract

References

  • [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.
  • [2] S.S. Dragomir, R.P. Agarwal and P. Cerone, On Simpson´ıs inequality and applications, J. of Inequal. Appl., 5(2000), 533-579.
  • [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.
  • [4] S.S. Dragomir, On Simpson’s quadrature formula for Lipschitzian mappings and applications Soochow J. Mathematics, 25 (1999), 175–180.
  • [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
  • [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.
  • [7] B.Z. Liu, An inequality of Simpson type, Proc. R. Soc. A, 461 (2005), 2155-2158.
  • [8] J. Pecaric, F. Proschan and Y.L. Tong, Convex functions, partial ordering and statistical applications, Academic Press, New York, 1991.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [20] N. Ujevic, Double integral inequalities of Simpson type and applications, J. Appl. Math. Comput., 14 (2004), no:1-2, p. 213-223.
  • [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.

Generalized Simpson Type Integral Inequalities

Year 2019, Volume: 7 Issue: 1, 186 - 191, 15.04.2019

Mehmet Zeki Sarıkaya Sakine Bardak

Abstract

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.


Keywords

Simpson type inequalities convex functions integral inequalities

References

  • [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.
  • [2] S.S. Dragomir, R.P. Agarwal and P. Cerone, On Simpson´ıs inequality and applications, J. of Inequal. Appl., 5(2000), 533-579.
  • [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.
  • [4] S.S. Dragomir, On Simpson’s quadrature formula for Lipschitzian mappings and applications Soochow J. Mathematics, 25 (1999), 175–180.
  • [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
  • [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.
  • [7] B.Z. Liu, An inequality of Simpson type, Proc. R. Soc. A, 461 (2005), 2155-2158.
  • [8] J. Pecaric, F. Proschan and Y.L. Tong, Convex functions, partial ordering and statistical applications, Academic Press, New York, 1991.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [20] N. Ujevic, Double integral inequalities of Simpson type and applications, J. Appl. Math. Comput., 14 (2004), no:1-2, p. 213-223.
  • [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.
There are 21 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mehmet Zeki Sarıkaya

Sakine Bardak This is me

Publication Date April 15, 2019
Submission Date March 13, 2019
Acceptance Date March 21, 2019
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Sarıkaya, M. Z., & Bardak, S. (2019). Generalized Simpson Type Integral Inequalities. Konuralp Journal of Mathematics, 7(1), 186-191.
AMA Sarıkaya MZ, Bardak S. Generalized Simpson Type Integral Inequalities. Konuralp J. Math. April 2019;7(1):186-191.
Chicago Sarıkaya, Mehmet Zeki, and Sakine Bardak. “Generalized Simpson Type Integral Inequalities”. Konuralp Journal of Mathematics 7, no. 1 (April 2019): 186-91.
EndNote Sarıkaya MZ, Bardak S (April 1, 2019) Generalized Simpson Type Integral Inequalities. Konuralp Journal of Mathematics 7 1 186–191.
IEEE M. Z. Sarıkaya and S. Bardak, “Generalized Simpson Type Integral Inequalities”, Konuralp J. Math., vol. 7, no. 1, pp. 186–191, 2019.
ISNAD Sarıkaya, Mehmet Zeki - Bardak, Sakine. “Generalized Simpson Type Integral Inequalities”. Konuralp Journal of Mathematics 7/1 (April 2019), 186-191.
JAMA Sarıkaya MZ, Bardak S. Generalized Simpson Type Integral Inequalities. Konuralp J. Math. 2019;7:186–191.
MLA Sarıkaya, Mehmet Zeki and Sakine Bardak. “Generalized Simpson Type Integral Inequalities”. Konuralp Journal of Mathematics, vol. 7, no. 1, 2019, pp. 186-91.
Vancouver Sarıkaya MZ, Bardak S. Generalized Simpson Type Integral Inequalities. Konuralp J. Math. 2019;7(1):186-91.
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