New generalized integral inequalities with applications

Artion Kashuri; Rozana Liko; Silvestru Sever Dragomir; Artion Kashuri; Rozana Liko; Silvestru Sever Dragomir

doi:10.3934/math.2019.3.984

AIMS Mathematics

2019, Volume 4, Issue 3: 984-996. doi: 10.3934/math.2019.3.984

Previous Article Next Article

Research article Special Issues

New generalized integral inequalities with applications

1.
Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, Vlora, Albania
2.
School of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia

Received: 06 March 2019 Accepted: 15 July 2019 Published: 31 July 2019
MSC : Primary: 26A51; Secondary: 26A33, 26D07, 26D10, 26D15

The authors have proved an identity for a generalized integral operator via differentiable function. By applying the established identity, the generalized trapezium type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results have been analyzed.
- Hermite-Hadamard inequality,
- general fractional integrals,
- Hölder’s inequality,
- power mean inequality
Citation: Artion Kashuri, Rozana Liko, Silvestru Sever Dragomir. New generalized integral inequalities with applications[J]. AIMS Mathematics, 2019, 4(3): 984-996. doi: 10.3934/math.2019.3.984

Related Papers:

Abstract

The authors have proved an identity for a generalized integral operator via differentiable function. By applying the established identity, the generalized trapezium type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results have been analyzed.

References

[1]	S. M. Aslani, M. R. Delavar and S. M. Vaezpour, Inequalities of Fejér type related to generalized convex functions with applications, Int. J. Anal. Appl., 16 (2018), 38-49.
[2]	F. X. Chen and S. H. Wu, Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl., 9 (2016), 705-716. doi: 10.22436/jnsa.009.02.32
[3]	Y. M. Chu, M. A. Khan, T. U. Khan, et al. Generalizations of Hermite-Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl., 9 (2016), 4305-4316. doi: 10.22436/jnsa.009.06.72
[4]	M. R. Delavar and M. De La Sen, Some generalizations of Hermite-Hadamard type inequalities, SpringerPlus, 5 (2016), 1-9. doi: 10.1186/s40064-015-1659-2
[5]	S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and trapezoidal formula, Appl. Math. Lett., 11 (1998), 91-95.
[6]	G. Farid and A. U. Rehman, Generalizations of some integral inequalities for fractional integrals, Ann. Math. silesianae, 31 (2017), 14.
[7]	M. A. Khan, Y. M. Chu, A. Kashuri, et al. New Hermite-Hadamard inequalities for conformable fractional integrals, J. Funct. Space., 2018 (2018), Article ID 6928130.
[8]	W. Liu, W. Wen and J. Park, Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals, J. Nonlinear Sci. Appl., 9 (2016), 766-777. doi: 10.22436/jnsa.009.03.05
[9]	C. Luo, T. S. Du, M. A. Khan, et al. Some k-fractional integrals inequalities through generalized λ_Φm-MT-preinvexity, J. Comput. Anal. Appl., 27 (2019), 690-705.
[10]	M. V. Mihai, Some Hermite-Hadamard type inequalities via Riemann-Liouville fractional calculus, Tamkang J. Math, 44 (2013), 411-416. doi: 10.5556/j.tkjm.44.2013.1218
[11]	S. Mubeen and G. M. Habibullah, k-Fractional integrals and applications, Int. J. Contemp. Math. Sci., 7 (2012), 89-94.
[12]	O. Omotoyinbo and A. Mogbodemu, Some new Hermite-Hadamard integral inequalities for convex functions, Int. J. Sci. Innovation Tech., 1 (2014), 1-12.
[13]	M. E. Özdemir, S. S. Dragomir and C. Yildiz, The Hadamard's inequality for convex function via fractional integrals, Acta Math. Sci., 33 (2013), 153-164.
[14]	M. Z. Sarikaya and F. Ertuğral, On the generalized Hermite-Hadamard inequalities, 2017. Available from: https://www.researchgate.net/publication/321760443.
[15]	M. Z. Sarikaya and H. Yildirim, On generalization of the Riesz potential, Indian J. Math. MathematicalSci., 3 (2007), 231-235.
[16]	E. Set, M. A. Noor, M. U. Awan, et al. Generalized Hermite-Hadamard type inequalities involving fractional integral operators, J. Inequal. Appl., 2017 (2017), 1-10. doi: 10.1186/s13660-016-1272-0
[17]	H. Wang, T. S. Du and Y. Zhang, k-fractional integral trapezium-like inequalities through (h,m)-convex and (α,m)-convex mappings, J. Inequal. Appl., 2017 (2017), 1-20. doi: 10.1186/s13660-016-1272-0
[18]	B. Y. Xi and F. Qi, Some integral inequalities of Hermite-Hadamard type for convex functionswith applications to means, J. Funct. Spaces Appl., 2012 (2012), Article ID 980438.
[19]	X. M. Zhang, Y. M. Chu and X. H. Zhang, The Hermite-Hadamard type inequality of GA-convex functions and its applications, J. Inequal. Appl., 2010 (2010), Article ID 507560.
[20]	Y. Zhang, T. S. Du, H. Wang, et al. Extensions of different type parameterized inequalities for generalized (m,h)-preinvex mappings via k-fractional integrals, J. Inequal. Appl., 2018 (2018), 1-30.

Reader Comments

Your name:*

Email:*
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)