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

Mehmet Kunt; Muhammad Amer Latıf; İmdat İşcan; Silvestru Sever Dragomır

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

Abstract

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.

Keywords

References

[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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Mehmet Kunt This is me
0000-0002-8730-5370
Türkiye

Muhammad Amer Latıf This is me
0000-0003-2349-3445
South Africa

İmdat İşcan This is me
0000-0001-6749-0591
Türkiye

Silvestru Sever Dragomır This is me
0000-0003-2902-6805
South Africa

Publication Date

March 1, 2019

Submission Date

April 13, 2018

Acceptance Date

January 21, 2019

Published in Issue

Year 2019 Volume: 37 Number: 1

IZ

https://izlik.org/JA56LX92WN

Cite

RIS / Bibtex

APA

Kunt, M., Latıf, M. A., İşcan, İ., & Dragomır, S. S. (2019). QUANTUM HERMITE-HADAMARD TYPE INEQUALITY AND SOME ESTIMATES OF QUANTUM MIDPOINT TYPE INEQUALITIES FOR DOUBLE INTEGRALS. Sigma Journal of Engineering and Natural Sciences, 37(1), 207-223. https://izlik.org/JA56LX92WN

AMA

1.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):207-223. https://izlik.org/JA56LX92WN

Chicago

Kunt, Mehmet, Muhammad Amer Latıf, İmdat İşcan, and Silvestru Sever Dragomır. 2019. “QUANTUM HERMITE-HADAMARD TYPE INEQUALITY AND SOME ESTIMATES OF QUANTUM MIDPOINT TYPE INEQUALITIES FOR DOUBLE INTEGRALS”. Sigma Journal of Engineering and Natural Sciences 37 (1): 207-23. https://izlik.org/JA56LX92WN.

EndNote

Kunt M, Latıf MA, İşcan İ, Dragomır SS (March 1, 2019) QUANTUM HERMITE-HADAMARD TYPE INEQUALITY AND SOME ESTIMATES OF QUANTUM MIDPOINT TYPE INEQUALITIES FOR DOUBLE INTEGRALS. Sigma Journal of Engineering and Natural Sciences 37 1 207–223.

IEEE

[1]M. Kunt, M. A. Latıf, İ. İşcan, and S. S. Dragomır, “QUANTUM HERMITE-HADAMARD TYPE INEQUALITY AND SOME ESTIMATES OF QUANTUM MIDPOINT TYPE INEQUALITIES FOR DOUBLE INTEGRALS”, SIGMA, vol. 37, no. 1, pp. 207–223, Mar. 2019, [Online]. Available: https://izlik.org/JA56LX92WN

ISNAD

Kunt, Mehmet - Latıf, Muhammad Amer - İşcan, İmdat - Dragomır, Silvestru Sever. “QUANTUM HERMITE-HADAMARD TYPE INEQUALITY AND SOME ESTIMATES OF QUANTUM MIDPOINT TYPE INEQUALITIES FOR DOUBLE INTEGRALS”. Sigma Journal of Engineering and Natural Sciences 37/1 (March 1, 2019): 207-223. https://izlik.org/JA56LX92WN.

JAMA

1.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;37:207–223.

MLA

Kunt, Mehmet, et al. “QUANTUM HERMITE-HADAMARD TYPE INEQUALITY AND SOME ESTIMATES OF QUANTUM MIDPOINT TYPE INEQUALITIES FOR DOUBLE INTEGRALS”. Sigma Journal of Engineering and Natural Sciences, vol. 37, no. 1, Mar. 2019, pp. 207-23, https://izlik.org/JA56LX92WN.

Vancouver

1.Mehmet Kunt, Muhammad Amer Latıf, İmdat İşcan, Silvestru Sever Dragomır. QUANTUM HERMITE-HADAMARD TYPE INEQUALITY AND SOME ESTIMATES OF QUANTUM MIDPOINT TYPE INEQUALITIES FOR DOUBLE INTEGRALS. SIGMA [Internet]. 2019 Mar. 1;37(1):207-23. Available from: https://izlik.org/JA56LX92WN