Generalizations of Hermite-Hadamard and Ostrowski type inequalities for MTm-preinvex functions

Authors

  • Artion Kashuri University Ismail Qemali.
  • Rozana Liko University Ismail Qemali.

DOI:

https://doi.org/10.4067/S0716-09172017000100004

Keywords:

Euler Gamma function, Euler Beta function, MT-convex function, Hermite-Hadamard type inequality, Ostrowski type inequality, Hölder’s inequality, power mean inequality, fractional integral, m-invex, P-function

Abstract

In the present paper, the notion of MTm-preinvex function is introduced and some new integral inequalities involving MTm-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard and Ostrowski type inequalities for MTm-preinvexfunctions via classical integrals and Riemann-Liouville fractional integrals are established. These results not only extends the results appeared in the literature (see [10], [11], [12]), but also provide new estimates on these types.

Author Biographies

Artion Kashuri, University Ismail Qemali.

Department of Mathematics, Faculty of Technical Science.

Rozana Liko, University Ismail Qemali.

Department of Mathematics, Faculty of Technical Science.

References

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[10] W. Liu, W. Wen, J. Park Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals J. Nonlinear Sci. Appl., 9, pp. 766-777, (2016).

[11] W. Liu, W. Wen, J. Park Ostrowski type fractional integral inequalities for MT-convex functions Miskolc Mathematical Notes., 16, 1, pp. 249-256, (2015).

[12] M. Tunç Ostrowski type inequalities for functions whose derivatives are MT-convex J. Comput. Anal. Appl., 17, 4, pp. 691-696, (2014).

Published

2017-04-06

How to Cite

[1]
A. Kashuri and R. Liko, “Generalizations of Hermite-Hadamard and Ostrowski type inequalities for MTm-preinvex functions”, Proyecciones (Antofagasta, On line), vol. 36, no. 1, pp. 45-80, Apr. 2017.

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