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QUANTUM HERMITE-HADAMARD TYPE INEQUALITY AND SOME ESTIMATES OF QUANTUM MIDPOINT TYPE INEQUALITIES FOR DOUBLE INTEGRALS

Yıl 2019, Cilt: 37 Sayı: 1, 207 - 223, 01.03.2019

Öz

In this paper, we give the correct quantum Hermite-Hadamard type inequality for the functions of two variables over finite rectangles. We provide some quantum estimates between the middle and the leftmost terms in correct quantum Hermite-Hadamard inequalities of functions of two variables using convexity and quasi-convexity on the co-ordinates.

Kaynakça

  • [1] Alp, N., Sarıkaya, M. Z., Kunt, M., İşcan, İ., q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Uni. Sci. 30 (2) (2018) 193-203.
  • [2] Dragomir, S. S., On Hadamard.s inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwan. J. Math. 4 (2001) 775.788.
  • [3] Ernst, T., A Comprehensive Treatment of q-Calculus, Springer Basel (2012).
  • [4] Gauchman, H., Integral inequalities in q-calculus, Comput. Math. Appl. 47 (2004) 281-300.
  • [5] Jackson, F. H., On a q-definite integrals, Quarterly J. Pure Appl. Math. 41 (1910) 193-203.
  • [6] Kac, V., Cheung, P., Quantum calculus, Springer (2001).
  • [7] Latif, M. A., Alomari, M., Hadamard-type inequalities for product of two convex functions on the co-ordinates. Int. Math. Forum 4 (47) (2009) 2327.2338.
  • [8] Latif, M. A., Dragomir, S. S., On some new inequalities for differentiable co-ordinated convex functions, J. Inequal. Appl., 28 (2012) 1-13.
  • [9] Latif, M. A., Hussain, S., Dragomir, S. S., New inequalities of Hermite-Hadamard type for co-ordinated quasi-convex functions, RGMIA Res. Rep. Collec., 14(2011), Article 54, 12 pp.
  • [10] Latif, M. A., Dragomir, S. S., Alomari, M., Some q-analogues of Hermite-Hadamard inequality of functions of two variables on finite rectangles in the plane, J. King Saud Uni.-Sci., 29 (3) (2017) 263-273.
  • [11] Noor, M. A., Noor, K.I., Awan, M. U., Some quantum estimates for Hermite-Hadamard inequalities, Appl. Math. Comput. 251 (2015) 675-679.
  • [12] Noor, M. A., Noor, K. I., Awan, M. U., Some quantum integral inequalities via preinvex functions, Appl. Math. Comput. 269 (2015) 242-251.
  • [13] Noor, M. A., Noor, K. I., Awan, M. U., Quantum analogues of Hermite-Hadamard type inequalities for generalized convexity, In: Daras, N., Rassias, M.T. (Eds.), Computation, Cryptography and Network Security, (2015) 413.439.
  • [14] Özdemir, M.E., Akdemir, A.O., Yıldız, C., On co-ordinated quasi-convex functions, Czechoslovak Math. J. 62 (137) (2012) 889-900.
  • [15] Sudsutad, W., Ntouyas, S. K., Tariboon, J., Quantum integral inequalities for convex functions, J. Math. Inequal. 9 (3) (2015) 781-793.
  • [16] Tariboon, J., Ntouyas, S. K., Quantum integral inequalities on finite intervals, J. Inequal. Appl. 121 (2014) 1-13.
  • [17] Tariboon, J., Ntouyas, S. K., Quantum calculus on finite intervals and applications to impulsive difference equations, Adv. Difference Equ. 282 (2013) 1-19.
  • [18] Zhuang, H., Liu, W., Park, J., Some quantum estimates of Hermite-Hadamard inequalities for quasi-convex functions, Mathematics, 7 (2) 152 (2019) 1-18.
Yıl 2019, Cilt: 37 Sayı: 1, 207 - 223, 01.03.2019

Öz

Kaynakça

  • [1] Alp, N., Sarıkaya, M. Z., Kunt, M., İşcan, İ., q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Uni. Sci. 30 (2) (2018) 193-203.
  • [2] Dragomir, S. S., On Hadamard.s inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwan. J. Math. 4 (2001) 775.788.
  • [3] Ernst, T., A Comprehensive Treatment of q-Calculus, Springer Basel (2012).
  • [4] Gauchman, H., Integral inequalities in q-calculus, Comput. Math. Appl. 47 (2004) 281-300.
  • [5] Jackson, F. H., On a q-definite integrals, Quarterly J. Pure Appl. Math. 41 (1910) 193-203.
  • [6] Kac, V., Cheung, P., Quantum calculus, Springer (2001).
  • [7] Latif, M. A., Alomari, M., Hadamard-type inequalities for product of two convex functions on the co-ordinates. Int. Math. Forum 4 (47) (2009) 2327.2338.
  • [8] Latif, M. A., Dragomir, S. S., On some new inequalities for differentiable co-ordinated convex functions, J. Inequal. Appl., 28 (2012) 1-13.
  • [9] Latif, M. A., Hussain, S., Dragomir, S. S., New inequalities of Hermite-Hadamard type for co-ordinated quasi-convex functions, RGMIA Res. Rep. Collec., 14(2011), Article 54, 12 pp.
  • [10] Latif, M. A., Dragomir, S. S., Alomari, M., Some q-analogues of Hermite-Hadamard inequality of functions of two variables on finite rectangles in the plane, J. King Saud Uni.-Sci., 29 (3) (2017) 263-273.
  • [11] Noor, M. A., Noor, K.I., Awan, M. U., Some quantum estimates for Hermite-Hadamard inequalities, Appl. Math. Comput. 251 (2015) 675-679.
  • [12] Noor, M. A., Noor, K. I., Awan, M. U., Some quantum integral inequalities via preinvex functions, Appl. Math. Comput. 269 (2015) 242-251.
  • [13] Noor, M. A., Noor, K. I., Awan, M. U., Quantum analogues of Hermite-Hadamard type inequalities for generalized convexity, In: Daras, N., Rassias, M.T. (Eds.), Computation, Cryptography and Network Security, (2015) 413.439.
  • [14] Özdemir, M.E., Akdemir, A.O., Yıldız, C., On co-ordinated quasi-convex functions, Czechoslovak Math. J. 62 (137) (2012) 889-900.
  • [15] Sudsutad, W., Ntouyas, S. K., Tariboon, J., Quantum integral inequalities for convex functions, J. Math. Inequal. 9 (3) (2015) 781-793.
  • [16] Tariboon, J., Ntouyas, S. K., Quantum integral inequalities on finite intervals, J. Inequal. Appl. 121 (2014) 1-13.
  • [17] Tariboon, J., Ntouyas, S. K., Quantum calculus on finite intervals and applications to impulsive difference equations, Adv. Difference Equ. 282 (2013) 1-19.
  • [18] Zhuang, H., Liu, W., Park, J., Some quantum estimates of Hermite-Hadamard inequalities for quasi-convex functions, Mathematics, 7 (2) 152 (2019) 1-18.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Articles
Yazarlar

Mehmet Kunt Bu kişi benim 0000-0002-8730-5370

Muhammad Amer Latıf Bu kişi benim 0000-0003-2349-3445

İmdat İşcan Bu kişi benim 0000-0001-6749-0591

Silvestru Sever Dragomır Bu kişi benim 0000-0003-2902-6805

Yayımlanma Tarihi 1 Mart 2019
Gönderilme Tarihi 13 Nisan 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 37 Sayı: 1

Kaynak Göster

Vancouver Kunt M, Latıf MA, İşcan İ, Dragomır SS. QUANTUM HERMITE-HADAMARD TYPE INEQUALITY AND SOME ESTIMATES OF QUANTUM MIDPOINT TYPE INEQUALITIES FOR DOUBLE INTEGRALS. SIGMA. 2019;37(1):207-23.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/