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

Fuat Usta; Hüseyin Budak; Fatma Ertugral; Mehmet Zeki Sarıkaya

doi:10.31801/cfsuasmas.463983

Araştırma Makalesi

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

Yıl 2019, Cilt: 68 Sayı: 1, 686 - 701, 01.02.2019

Fuat Usta Hüseyin Budak Fatma Ertugral Mehmet Zeki Sarıkaya

https://doi.org/10.31801/cfsuasmas.463983

Cited By: 6

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.

Anahtar Kelimeler

Fractional integral operators, Hermite-Hadamard inequality, midpoint inequality, convex function

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

Fuat Usta Hüseyin Budak Fatma Ertugral Mehmet Zeki Sarıkaya

https://doi.org/10.31801/cfsuasmas.463983

Cited By: 6

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.