ON HARDY TYPE INEQUALITIES VIA K-FRACTIONAL INTEGRALS

Yıl 2020, Cilt: 10 Sayı: 2, 443 - 451, 01.03.2020

M. Z. Sarıkaya C. C. Bılışık T. Tunç

Öz

In this study, we will give the k-fractional integral inequalities to take advantage of the some results of Hardy type inequalities and some special cases.

Anahtar Kelimeler

H¨older’s inequality, k-fractional integrals, Hardy inequality

Kaynakça

• Abramovich, S., Knlic, K., Pecacard, J. and Presson, E., (2010), Some new refined Hardy type inequalities with general Kernels and measures, Aequat. Math., 79(1-2), pp. 157-172.
• Diaz, R. and Pariguan, E., (2007), On hypergeometric functions and Pochhammer k symbol, Divulg. Math, 15, pp. 179-192.
• Diaz, R., Ortiz, C. and Pariguan, E., (2010), On the k -gamma q -distribution, Cent. Eur. J. Math., , (3) , pp. 448-458.
• Hardy, G. H., Littlewood, J. E. and Polya, G., (1952), Inequalities, 2nd Ed. Cambridge Univ.
• Hardy, G. H., (1920), Note on a theorem of Hilbert, Math.Z., 6, (3-4), pp. 314-317.
• Hardy, G. H., (1928), Notes on some points in the integral calculus, Messenger Math., 57 , pp. 12-16.
• Khameli, A., Dahmani, Z., Freha, K. and Sarıkaya, M. Z., (2016), New- Riemann- Liouville general- izations for some inequalities of Hardy type, Malaya J. Mat., 4, (2), pp. 277-283.
• Kokologiannaki, C. G., (2010), Properties and inequalities of generalized k - gamma, beta and zeta functions, Int. J. Contemp. Math. Sciences, 5, (14) , pp. 653-660.
• Levinson, N., (1964), Generalizations of an inequality of Hardy, Duke Math. J., 31 , pp. 389-394.
• Mubeen, S. and Habibullah, G. M., (2012), k -fractional integrals and application, Int. J. Contemp. Math. Sciences, 7(2), pp. 89-94.
• Romero, L. G., Luque, L.L., Dorrego, G. A. and Cerutti, R. A., (2013), On the k -Riemann-Liouville fractional derivative, Int. J. Contemp. Math. Sciences, 8(1-4), pp. 41-51.
• Sarikaya, M. Z. and Yildirim, H., (2006), Some Hardy type integral inequalities, JIPAM Journal, 7(5), Art. 178, , pp. 1-5.
• Sarikaya, M. Z. and Karaca, A., (2014), On the k-Riemann-Liouville fractional integral and applica- tions, International Journal of Mathematics and Statistics, 1, (3), pp. 33-43.
• Sroysang, B., (2013), A generalization of some integral inequalities similar to Hardy’s inequality, Math. Aeterna, 3, pp. 593-593.
• Sulaiman, W. T., (2012), Minkowski’s H¨older’s and Hardy’s integral inequalities, Int. J. Mod. Math. Sci., 1, (1), pp. 14-24.
• Wu, S., Sroysang, B. and Li, S., (2016), A further generalization of certain integral inequalities similar to Hardy’s inequality, J. Nonlinear Sci. Appl., 9, pp. 1093-1102.