Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals

Year 2016, Volume: 4 Issue: 1, 77 - 87, 15.04.2016

İmdat İşcan

https://doi.org/10.36753/mathenot.421413

Cited By: 5

Abstract

In this paper, the author establishes some Hadamard-type and Bullen-type inequalities for Lipschitzian
functions via Riemann Liouville fractional integral.

Keywords

Lipschitzian functions, Hadamard inequality, Bullen inequality, Riemann–Liouville fractional integral

References

• [1] Dahmani, Z., On Minkowski and Hermite-Hadamard integral inequalities via fractional via fractional integration. Ann. Funct. Anal. 1 (2010), no. 1, 51-58.
• [2] Dragomir, S.S., Cho, Y.J. and Kim, S.S., Inequalities of Hadamard’s Type for Lipschitzian Mappings and Their Applications. J. Math. Anal. Appl. 245 (2000), 489-501.
• [3] Hwang, S.-R., Hsu, K.-C. and Tseng, K.-L., Hadamard-type inequalities for Lipschitzian functions in one and two variables with applications. J. Math. Anal. Appl. 405 (2013), 546-554.
• [4]İşcan, İ., New general integral inequalities for Lipschitzian functions via Hadamard fractional integrals. Int. J. Anal. 2014 (2014), Article ID 353924, 8 pages.
• [5] Samko, S.G., Kilbas, A.A. and Marichev, O.I., Fractional Integrals and Derivatives Theory and Application. Gordan and Breach Science, New York, 1993.
• [6] Sarıkaya, M.Z. and Ogunmez, H., On new inequalities via Riemann-Liouville fractional integration. Abstr. Appl. Anal. 2012 (2012), Article ID 428983, 10 pages.
• [7] Sarıkaya, M.Z., Set, E., Yaldız, H. and Başak, N., Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities. Math. Comput. Modelling 57 (2013), 2403-2407.
• [8] Tseng, K.-L., Hwang, S.-R. and Dragomir, S.S., Fejér-type inequalities (1). J. Inequal. Appl. 2010 (2010), Article ID 531976, 7 pages.
• [9] Tseng, K.-L., Hwang, S.-R. and Hsu, K.-C., Hadamard-type and Bullen-type inequalities for Lipschitzian functions and their applications. Comput. Math. Appl. 64 (2012), no. 4, 651-660.
• [10] Yang, G.-S. and Tseng, K.-L., Inequalities of Hadamard’s Type for Lipschitzian Mappings. J. Math. Anal. Appl. 260 (2001), no. 1, 230-238.
• [11] Zhu, C., Feckan, M. and Wang, J., Fractional integral inequalities for differentiable convex mappings and applications to special means and a midpoint formula. J. Appl. Math. Stat. Inform. 8 (2012), no. 2, 21-28.