HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS

Abstract

In this paper, the authors have obtained some new developments of Hermite- Hadamard type inequalities for generalized fractional integrals dened by Akkurt et al. [1]. With the help of this fractional integral denition, some new original results have been obtained, which include many studies in the literature.

Keywords

• Fractional integrals,Hermite-Hadamard inequality

References

1. A. Akkurt, M. E. Yıldırım and H. Yıldırım, On some Integral Inequalities for (k,h)-Riemann-Liouville fractional integral, New Trends in Mathematical Sciences (NTMSCI), 4(1), (2016), 138-146. H. Fehmi Gidergelmez, A. Akkurt and H. Yıldırım, Hermite-Hadamard type inequalities for Generalized Fractional Integrals via Strongly Convex Functions, (Submitted.). Polyak, B.T.: Existence theorems and convergence of minimizing sequences in extremum problems with restrictions. Sov. Math. Dokl. 7, 72{75 (1966)Kilbas, A. A., Srivastava, H.M., and Trujillo, J.J., Theory and Applications of Fractional Diferential Equations, Elsevier B.V., Amsterdam, Netherlands, 2006.Samko SG, Kilbas AA, Marichev OI. Fractional Integrals and Derivatives-Theory and Applications, Gordon and Breach, Linghorne, 1993.Mubeen, S., Iqbal, S., and Muharrem Tomar, M., On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function and k-parameter, J. Inequal. Math. Appl.1(2016), 1-9.Diaz, R. and Pariguan, E., On hypergeometric functions and Pochhammer ksymbol, Divulg. Math, 15.(2007),179-192.U.N. Katugampola, New Approach to a Generalized Fractional Fntegral, Appl. Math. Comput. 218(3), (2011), 860-865.Chen, H., Katugampola, U.N.: Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for generalized fractional integrals. J. Math. Anal. Appl. 446, 1274{1291 (2017).Mubeen, S. and Habibullah, G.M., kfractional integrals and application, Int. J. Contemp.Math. Sciences, 7(2), 2012, 89-94.M.Z. Sarikaya, Z. Dahmani, M.E. Kiris and F. Ahmad, (k; s)Riemann-Liouville fractional integral and applications, Hacettepe Journal of Mathematics and Statistics, Accepted.Sarikaya, M.Z., Set, E., Yaldiz, H., Basak, N.: Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities. Math. Comput. Modell. 57(9), 2403{2407 (2013)