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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)

Details

Primary Language English
Subjects Mathematics
Journal Section Research Article
Authors

Abdullah AKKURT (Primary Author)
KAHRAMANMARAŞ SÜTÇÜ İMAM ÜNİVERSİTESİ
0000-0001-5644-1276
Türkiye


H. Fehmi GIDERGELMEZ
Kahramanmaras Sütcü Imam University
Türkiye


Seda KILINC This is me
Kahramanmaras Sütcü Imam University
Türkiye


Hüseyin YILDIRIM
Kahramanmaras Sütcü Imam University
0000-0001-8855-9260
Türkiye

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

Cite

Bibtex @research article { jum506489, journal = {Journal of Universal Mathematics}, issn = {2618-5660}, eissn = {2618-5660}, address = {editorinchief@junimath.com}, publisher = {Gökhan ÇUVALCIOĞLU}, year = {2019}, volume = {2}, pages = {51 - 59}, doi = {10.33773/jum.506489}, title = {HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS}, key = {cite}, author = {Akkurt, Abdullah and Gıdergelmez, H. Fehmi and Kılınc, Seda and Yıldırım, Hüseyin} }
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 . DOI: 10.33773/jum.506489
MLA Akkurt, A. , Gıdergelmez, H. F. , Kılınc, S. , Yıldırım, H. "HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS" . Journal of Universal Mathematics 2 (2019 ): 51-59 <https://dergipark.org.tr/en/pub/jum/issue/42856/506489>
Chicago Akkurt, A. , Gıdergelmez, H. F. , Kılınc, S. , Yıldırım, H. "HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS". Journal of Universal Mathematics 2 (2019 ): 51-59
RIS TY - JOUR T1 - HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS AU - Abdullah Akkurt , H. Fehmi Gıdergelmez , Seda Kılınc , Hüseyin Yıldırım Y1 - 2019 PY - 2019 N1 - doi: 10.33773/jum.506489 DO - 10.33773/jum.506489 T2 - Journal of Universal Mathematics JF - Journal JO - JOR SP - 51 EP - 59 VL - 2 IS - 1 SN - 2618-5660-2618-5660 M3 - doi: 10.33773/jum.506489 UR - https://doi.org/10.33773/jum.506489 Y2 - 2019 ER -
EndNote %0 Journal of Universal Mathematics HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS %A Abdullah Akkurt , H. Fehmi Gıdergelmez , Seda Kılınc , Hüseyin Yıldırım %T HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS %D 2019 %J Journal of Universal Mathematics %P 2618-5660-2618-5660 %V 2 %N 1 %R doi: 10.33773/jum.506489 %U 10.33773/jum.506489
ISNAD Akkurt, Abdullah , Gıdergelmez, H. Fehmi , Kılınc, Seda , Yıldırım, Hüseyin . "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
AMA Akkurt A. , Gıdergelmez H. F. , Kılınc S. , Yıldırım H. HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS. JUM. 2019; 2(1): 51-59.
Vancouver Akkurt A. , Gıdergelmez H. F. , Kılınc S. , Yıldırım H. HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS. Journal of Universal Mathematics. 2019; 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", Journal of Universal Mathematics, vol. 2, no. 1, pp. 51-59, Jan. 2019, doi:10.33773/jum.506489