Research Article

The Minkowski's inequalities utilizing newly defined generalized fractional integral operators

Volume: 68 Number: 1 February 1, 2019
EN

The Minkowski's inequalities utilizing newly defined generalized fractional integral operators

Abstract

Motivated by the recent generalized fractional integral operators proposed by Tunc et. al. <cite>tunc</cite>, we establish a generalization of the reverse Minkowski's inequalities. Within this context, we provide new upper bounds of inequalities utilizing generalized fractional integral operators and show and state other inequalities related to this fractional integral operator.

Keywords

References

  1. R. P. Agarwal, M.-J. Luo and R. K. Raina, On Ostrowski type inequalities, Fasciculi Mathematici, 24, De Gruyter, (2016) doi:10.1515/fascmath-2016-0001.
  2. P. Agarwal and J. E. Restrepo, An extension by means of ω-weighted classes of the generalized Riemann-Liouville k-fractional integral inequalities, (pending).
  3. A. Akkurt, M. E. Yıldırım, and H. Yıldırım, On some integral inequalities for (k,h)-Riemann-Liouville fractional integral, New Trends in Mathematical Science, 4 (2016), no. 2, 138--138.
  4. L. Bougoffa, On Minkowski and Hardy integral inequality, J. Inequal. Pure and Appl. Math. 7 (2006).
  5. V.L. Chinchane, New approach to Minkowski fractional inequalities using generalized kfractional integral operator, arXiv:1702.05234v1 [math.CA].
  6. V.L. Chinchane and D. B. Pachpatte, New fractional inequalities via Hadamard fractional integral, Internat. J. Functional Analyisis, Operator Theory and Application, 5(3)(2013), 165-176.
  7. Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(1)(2010), 51-58.
  8. R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k symbol, Divulg.Math, 15, (2007), 179- 192.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

February 1, 2019

Submission Date

December 12, 2017

Acceptance Date

April 6, 2018

Published in Issue

Year 2019 Volume: 68 Number: 1

APA
Usta, F., Budak, H., Ertugral, F., & Sarıkaya, M. Z. (2019). The Minkowski’s inequalities utilizing newly defined generalized fractional integral operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 686-701. https://doi.org/10.31801/cfsuasmas.463983
AMA
1.Usta F, Budak H, Ertugral F, Sarıkaya MZ. The Minkowski’s inequalities utilizing newly defined generalized fractional integral operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):686-701. doi:10.31801/cfsuasmas.463983
Chicago
Usta, Fuat, Hüseyin Budak, Fatma Ertugral, and Mehmet Zeki Sarıkaya. 2019. “The Minkowski’s Inequalities Utilizing Newly Defined Generalized Fractional Integral Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (1): 686-701. https://doi.org/10.31801/cfsuasmas.463983.
EndNote
Usta F, Budak H, Ertugral F, Sarıkaya MZ (February 1, 2019) The Minkowski’s inequalities utilizing newly defined generalized fractional integral operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 686–701.
IEEE
[1]F. Usta, H. Budak, F. Ertugral, and M. Z. Sarıkaya, “The Minkowski’s inequalities utilizing newly defined generalized fractional integral operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 686–701, Feb. 2019, doi: 10.31801/cfsuasmas.463983.
ISNAD
Usta, Fuat - Budak, Hüseyin - Ertugral, Fatma - Sarıkaya, Mehmet Zeki. “The Minkowski’s Inequalities Utilizing Newly Defined Generalized Fractional Integral Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 1, 2019): 686-701. https://doi.org/10.31801/cfsuasmas.463983.
JAMA
1.Usta F, Budak H, Ertugral F, Sarıkaya MZ. The Minkowski’s inequalities utilizing newly defined generalized fractional integral operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:686–701.
MLA
Usta, Fuat, et al. “The Minkowski’s Inequalities Utilizing Newly Defined Generalized Fractional Integral Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, Feb. 2019, pp. 686-01, doi:10.31801/cfsuasmas.463983.
Vancouver
1.Fuat Usta, Hüseyin Budak, Fatma Ertugral, Mehmet Zeki Sarıkaya. The Minkowski’s inequalities utilizing newly defined generalized fractional integral operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019 Feb. 1;68(1):686-701. doi:10.31801/cfsuasmas.463983

Cited By

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.