Some New Hermite-Hadamard Type Inequalities for Convex Functions

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Islamic Republic of Iran.

10.22072/wala.2020.117932.1260

Abstract

Convex sets and convex functions play a fundamental role in the development of various fields
of pure and applied mathematics.  Recently, many new generalizations of inequalities with respect to Hermite-Hadamard  have been proposed in the literature. In this paper,  some  new  inequalities of the Hermite-Hadamard type for differentiable convex functions are given. These new inequalities are based on the second derivative functions.

Keywords

References

[1] M. Adil Khan, Y.-M. Chu, T.U. Khan and J. Khan,  Some inequalities of Hermite-Hadamard type for $S$-convex functions with applications, Open Math., 15 (2017), 1414-1430.
[2] H. Barsam and A.R. Sattarzadeh, Some results on Hermite-Hadamard inequalities, J. Mahani Math. Res. Cent., 9(2) (2020), 79-86.
[3] H. Barsam and M. Ramezani, Some results on Hermite-Hadamard type inequalities with respect to fractional integrals, Casp. J. Math. Sci., (2020), doi:10.22080/cjms.2020.17502.1437.
[4] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
[5] S.S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal  formula, Appl. Math. Lett., 11 (1998), 91-95.
[6] H. Kavurmaci, M. Avci and  M.E. Ozdemir,  New inequalities of Hermite-Hadamard type for convex functions with applications, J. Inequal. Appl., 86 (2011), 1-10.
[7] M.E. Ozdemir, M. Avci and E. Set,  On some inequalities of Hermite-Hadamard type via $m$-convexity, Appl. Math. Lett., 23(9) (2010), 1065-1070.
[8] G. Toader, Some generalizations of the convexity, Proceedings of the Colloquium on Approximation and Optimization, (1984), 329-338.
Wavelet and Linear Algebra
Volume 7, Issue 2
Autumn
2020
Pages 11-22

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