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.
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)
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)
Akkurt, A., Gıdergelmez, H. F., Kılınc, S., Yıldırım, H. (2019). HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS. Journal of Universal Mathematics, 2(1), 51-59. https://doi.org/10.33773/jum.506489
AMA
Akkurt A, Gıdergelmez HF, Kılınc S, Yıldırım H. HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS. JUM. January 2019;2(1):51-59. doi:10.33773/jum.506489
Chicago
Akkurt, Abdullah, H. Fehmi Gıdergelmez, Seda Kılınc, and Hüseyin Yıldırım. “HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-H)-FRACTIONAL INTEGRALS”. Journal of Universal Mathematics 2, no. 1 (January 2019): 51-59. https://doi.org/10.33773/jum.506489.
EndNote
Akkurt A, Gıdergelmez HF, Kılınc S, Yıldırım H (January 1, 2019) HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS. Journal of Universal Mathematics 2 1 51–59.
IEEE
A. Akkurt, H. F. Gıdergelmez, S. Kılınc, and H. Yıldırım, “HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS”, JUM, vol. 2, no. 1, pp. 51–59, 2019, doi: 10.33773/jum.506489.
ISNAD
Akkurt, Abdullah et al. “HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-H)-FRACTIONAL INTEGRALS”. Journal of Universal Mathematics 2/1 (January 2019), 51-59. https://doi.org/10.33773/jum.506489.
JAMA
Akkurt A, Gıdergelmez HF, Kılınc S, Yıldırım H. HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS. JUM. 2019;2:51–59.
MLA
Akkurt, Abdullah et al. “HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-H)-FRACTIONAL INTEGRALS”. Journal of Universal Mathematics, vol. 2, no. 1, 2019, pp. 51-59, doi:10.33773/jum.506489.
Vancouver
Akkurt A, Gıdergelmez HF, Kılınc S, Yıldırım H. HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS. JUM. 2019;2(1):51-9.