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

Year 2019, Volume: 2 Issue: 1, 51 - 59, 30.01.2019
https://doi.org/10.33773/jum.506489

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.

References

  • 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)
Year 2019, Volume: 2 Issue: 1, 51 - 59, 30.01.2019
https://doi.org/10.33773/jum.506489

Abstract

References

  • 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)
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Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Abdullah Akkurt

H. Fehmi Gıdergelmez

Seda Kılınc This is me

Hüseyin Yıldırım

Publication Date January 30, 2019
Submission Date January 2, 2019
Acceptance Date January 22, 2019
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA 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.