Korean J. Math. Vol. 27 No. 2 (2019) pp.279-295
DOI: https://doi.org/10.11568/kjm.2019.27.2.279

On new inequalities of Simpson's type for generalized convex functions

Article Sidebar

PDF
Published: Jun 30, 2019
Keywords:
Simpsonx92s inequality, local fractional integral, fractal space, generalized convex function
Mathematics Subject Classification:
SimpsonÂ’s inequality, 26D15, 26D10.

Main Article Content

Mehmet Zeki Sarıkaya
Department of Mathematics, Faculty of Science and Arts Duzce University, Konuralp Campus, Duzce, Turkey
Huseyin Budak
Department of Mathematics, Faculty of Science and Arts Du ̈zce University, Konuralp Campus, Du ̈zce, Turkey
Samet Erden
Department of Mathematics, Faculty of Science, Bartın University, Bartin, Turkey

Abstract

In this paper, using local fractional integrals on fractal sets $R^{\alpha }$ $\left( 0<\alpha \leq 1\right) $ of real line numbers, we establish new some inequalities of Simpson's type based on generalized convexity.



Article Details

References

[1] M. W. 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), Article 9. [Online:http://ajmaa.org/RGMIA/v12n4.php] Google Scholar

[2] G-S. Chen, Generalizations of H ̈older’s and some related integral inequalities on fractal space, Journal of Function Spaces and Applications Volume 2013, Article ID 198405, 9 pages. Google Scholar

[3] S. S. Dragomir, R. P. Agarwal and P. Cerone, On Simpson’s inequality and applications, J. of Inequal. Appl. 5 (2000), 533–579. Google Scholar

[4] B. Z. Liu, An inequality of Simpson type, Proc. R. Soc. A 461 (2005), 2155–2158. Google Scholar

[5] H. Mo, X Sui and D Yu, Generalized convex functions on fractal sets and two related inequalities, Abstract and Applied Analysis, Volume 2014, Article ID 636751, 7 pages. Google Scholar

[6] J. Park, Generalization of some Simpson-like type inequalities via differentiable s-convex mappings in the second sense, Inter. Journ. of Math.and Math. Sci 2011 (2011), Article ID: 493531, 13 pages. Google Scholar

[7] J. Park, Hermite and Simpson-like type inequalities for functions whose second derivatives in absolute values at certain power are s-convex, Int. J. Pure Appl. Math. (2012), 587–604. Google Scholar

[8] M. Z. Sarikaya, E. Set and M. E. O ̈zdemir, On new inequalities of Simpson’s type for convex functions, RGMIA Res. Rep. Coll. 13 (2) (2010), Article2. Google Scholar

[9] J. Yang, D. Baleanu and X. J. Yang, Analysis of fractal wave equations by local fractional Fourier series method, Adv. Math. Phys. , 2013 (2013), Article ID 632309. Google Scholar

[10] X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, 2012. Google Scholar

[11] X. J. Yang, Local fractional integral equations and their applications, Advances in Computer Science and its Applications (ACSA) 1 (4), 2012. Google Scholar

[12] X. J. Yang, Generalized local fractional Taylor’s formula with local fractional derivative, Journal of Expert Systems, 1 (1) (2012), 26-30. Google Scholar

[13] X. J. Yang, Local fractional Fourier analysis, Advances in Mechanical Engineering and its Applications 1 (1) (2012), 12-16. Google Scholar