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

Yıl 2019, Cilt: 68 Sayı: 1, 686 - 701, 01.02.2019
https://doi.org/10.31801/cfsuasmas.463983

Öz

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.

Kaynakça

  • 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.
  • P. Agarwal and J. E. Restrepo, An extension by means of ω-weighted classes of the generalized Riemann-Liouville k-fractional integral inequalities, (pending).
  • 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.
  • L. Bougoffa, On Minkowski and Hardy integral inequality, J. Inequal. Pure and Appl. Math. 7 (2006).
  • V.L. Chinchane, New approach to Minkowski fractional inequalities using generalized kfractional integral operator, arXiv:1702.05234v1 [math.CA].
  • 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.
  • Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(1)(2010), 51-58.
  • R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k symbol, Divulg.Math, 15, (2007), 179- 192.
  • U. Katugampola, New approach to a generalized fractional integral, Applied Mathematics and Computation (2011).xxxxxxxxxxx
  • U. Katugampola, On Generalized Fractional Integrals and Derivatives, Ph.D. Dissertation, Southern Illinois University, Carbondale, August, 2011.
  • R. Khalil, M. Al horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264 (2014), 65-70.
  • A. A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Diferential Equations, Elsevier B.V., Amsterdam, Netherlands, 2006.
  • V. Kiryakova, On two Saigos fractional integral operator in the class of univalent functions, Fract. Calc. Appl. Anal., 9(2)(2006), 159-176.
  • H. Kober, On fractional integrals and derivatives, The Quarterly Journal of Mathematics (Oxford Series), (1940). xxxxxxxxxxxxxxx
  • S. Mubeen and G. M. Habibullah, k-Fractional integrals and applications, International Journal of Contemporary Mathematical Sciences, 7(2012), 89--94.
  • E. Set, M. Tomar, M. Sarikaya, On generalized Gruss type inequalities for k-fractional integrals, Appl. Math. Comput. (2015) xxxxxxxxxxxxxxx
  • M. Saigo, A remark on integral operators involving the Gauss hypergeometric function, Rep. College General Ed., Kyushu Univ., 11 (1978), 135-143.
  • M. Sarikaya, Z. Dahmani, M. Kiris, F. Ahmad, (k; s)-Riemann-Liouville fractional integral and applications, Hacet. J. Math. Stat., (2016) xxxxxxxxxxxxxxxxx
  • B. Sroysang, More on Reverses of Minkowskis Integral Inequality, Mathematica Aeterna, Vol. 3, (2013), no. 7, 597-600.
  • W. T. Sulaiman, Reverses of Minkowski's, Hölder's, and Hardy's integral inequalities, Int. J. Mod. Math. Sci., (2012), 1(1), 1424.
  • R.K. Raina, On generalized Wright's hypergeometric functions and fractional calculus operators, East Asian Math. J., 21(2) (2005), 191-203.
  • T. Tunç, H. Budak, F. Usta, M. Z. Sarikaya, On new generalized fractional integral operators and related fractional inequalities, ResearchGate Article, Available online at: https://www.researchgate.net/publication/313650587.
Yıl 2019, Cilt: 68 Sayı: 1, 686 - 701, 01.02.2019
https://doi.org/10.31801/cfsuasmas.463983

Öz

Kaynakça

  • 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.
  • P. Agarwal and J. E. Restrepo, An extension by means of ω-weighted classes of the generalized Riemann-Liouville k-fractional integral inequalities, (pending).
  • 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.
  • L. Bougoffa, On Minkowski and Hardy integral inequality, J. Inequal. Pure and Appl. Math. 7 (2006).
  • V.L. Chinchane, New approach to Minkowski fractional inequalities using generalized kfractional integral operator, arXiv:1702.05234v1 [math.CA].
  • 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.
  • Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(1)(2010), 51-58.
  • R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k symbol, Divulg.Math, 15, (2007), 179- 192.
  • U. Katugampola, New approach to a generalized fractional integral, Applied Mathematics and Computation (2011).xxxxxxxxxxx
  • U. Katugampola, On Generalized Fractional Integrals and Derivatives, Ph.D. Dissertation, Southern Illinois University, Carbondale, August, 2011.
  • R. Khalil, M. Al horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264 (2014), 65-70.
  • A. A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Diferential Equations, Elsevier B.V., Amsterdam, Netherlands, 2006.
  • V. Kiryakova, On two Saigos fractional integral operator in the class of univalent functions, Fract. Calc. Appl. Anal., 9(2)(2006), 159-176.
  • H. Kober, On fractional integrals and derivatives, The Quarterly Journal of Mathematics (Oxford Series), (1940). xxxxxxxxxxxxxxx
  • S. Mubeen and G. M. Habibullah, k-Fractional integrals and applications, International Journal of Contemporary Mathematical Sciences, 7(2012), 89--94.
  • E. Set, M. Tomar, M. Sarikaya, On generalized Gruss type inequalities for k-fractional integrals, Appl. Math. Comput. (2015) xxxxxxxxxxxxxxx
  • M. Saigo, A remark on integral operators involving the Gauss hypergeometric function, Rep. College General Ed., Kyushu Univ., 11 (1978), 135-143.
  • M. Sarikaya, Z. Dahmani, M. Kiris, F. Ahmad, (k; s)-Riemann-Liouville fractional integral and applications, Hacet. J. Math. Stat., (2016) xxxxxxxxxxxxxxxxx
  • B. Sroysang, More on Reverses of Minkowskis Integral Inequality, Mathematica Aeterna, Vol. 3, (2013), no. 7, 597-600.
  • W. T. Sulaiman, Reverses of Minkowski's, Hölder's, and Hardy's integral inequalities, Int. J. Mod. Math. Sci., (2012), 1(1), 1424.
  • R.K. Raina, On generalized Wright's hypergeometric functions and fractional calculus operators, East Asian Math. J., 21(2) (2005), 191-203.
  • T. Tunç, H. Budak, F. Usta, M. Z. Sarikaya, On new generalized fractional integral operators and related fractional inequalities, ResearchGate Article, Available online at: https://www.researchgate.net/publication/313650587.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Fuat Usta 0000-0002-7750-6910

Hüseyin Budak 0000-0002-7750-6910

Fatma Ertugral Bu kişi benim 0000-0002-7561-8388

Mehmet Zeki Sarıkaya 0000-0002-6165-9242

Yayımlanma Tarihi 1 Şubat 2019
Gönderilme Tarihi 12 Aralık 2017
Kabul Tarihi 6 Nisan 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

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 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. Şubat 2019;68(1):686-701. doi:10.31801/cfsuasmas.463983
Chicago Usta, Fuat, Hüseyin Budak, Fatma Ertugral, ve Mehmet Zeki Sarıkaya. “The Minkowski’s Inequalities Utilizing Newly Defined Generalized Fractional Integral Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 686-701. https://doi.org/10.31801/cfsuasmas.463983.
EndNote Usta F, Budak H, Ertugral F, Sarıkaya MZ (01 Şubat 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 F. Usta, H. Budak, F. Ertugral, ve M. Z. Sarıkaya, “The Minkowski’s inequalities utilizing newly defined generalized fractional integral operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 686–701, 2019, doi: 10.31801/cfsuasmas.463983.
ISNAD Usta, Fuat vd. “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 (Şubat 2019), 686-701. https://doi.org/10.31801/cfsuasmas.463983.
JAMA 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 vd. “The Minkowski’s Inequalities Utilizing Newly Defined Generalized Fractional Integral Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 686-01, doi:10.31801/cfsuasmas.463983.
Vancouver 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.

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

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