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

Yıl 2019, Cilt: 2 Sayı: 1, 51 - 59, 30.01.2019
https://doi.org/10.33773/jum.506489

Öz

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.

Kaynakça

  • 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)
Yıl 2019, Cilt: 2 Sayı: 1, 51 - 59, 30.01.2019
https://doi.org/10.33773/jum.506489

Öz

Kaynakça

  • 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)
Toplam 1 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Abdullah Akkurt

H. Fehmi Gıdergelmez

Seda Kılınc Bu kişi benim

Hüseyin Yıldırım

Yayımlanma Tarihi 30 Ocak 2019
Gönderilme Tarihi 2 Ocak 2019
Kabul Tarihi 22 Ocak 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 1

Kaynak Göster

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. Ocak 2019;2(1):51-59. doi:10.33773/jum.506489
Chicago Akkurt, Abdullah, H. Fehmi Gıdergelmez, Seda Kılınc, ve Hüseyin Yıldırım. “HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-H)-FRACTIONAL INTEGRALS”. Journal of Universal Mathematics 2, sy. 1 (Ocak 2019): 51-59. https://doi.org/10.33773/jum.506489.
EndNote Akkurt A, Gıdergelmez HF, Kılınc S, Yıldırım H (01 Ocak 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, ve H. Yıldırım, “HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-h)-FRACTIONAL INTEGRALS”, JUM, c. 2, sy. 1, ss. 51–59, 2019, doi: 10.33773/jum.506489.
ISNAD Akkurt, Abdullah vd. “HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-H)-FRACTIONAL INTEGRALS”. Journal of Universal Mathematics 2/1 (Ocak 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 vd. “HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (k-H)-FRACTIONAL INTEGRALS”. Journal of Universal Mathematics, c. 2, sy. 1, 2019, ss. 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.