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ON HARDY TYPE INEQUALITIES VIA K-FRACTIONAL INTEGRALS

Year 2020, Volume: 10 Issue: 2, 443 - 451, 01.03.2020

Abstract

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.

References

  • 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.
Year 2020, Volume: 10 Issue: 2, 443 - 451, 01.03.2020

Abstract

References

  • 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.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

M. Z. Sarıkaya This is me

C. C. Bılışık This is me

T. Tunç This is me

Publication Date March 1, 2020
Published in Issue Year 2020 Volume: 10 Issue: 2

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