Trapezoid Inequalities for Twice Differentiable Mappings
Abstract
This study introduces a new identity to derive alternative results for the inequality in (1.1) and compares them with previous findings. Additionally, new trapezoid inequalities are developed using the convexity of second-order derivatives' absolute values.
Keywords
Convex function, Hermite-Hadamard inequalities, Hölder inequality, Trapezoid inequality
References
- [1] S. S. Dragomir, P. Cerone, A. Sofo, Some remarks on the trapezoid rule in numerical integration, RGMIA research report collection, 2(5) (1999).
- [2] S. S. Dragomir, A. Sofo, An integral inequality for twice differentiable mappings and applications, Tamkang J. Math., 31(4) (2000), 257-266.
- [3] M. Z. Sarıkaya, E. Set, M. Emin Ozdemir, On some integral inequalities for twice differentiable mappings, Studia Univ. Babes, Bolyai Math., 59(1) (2014), 11-24.
- [4] X. L. Cheng, J. Sun, A note on the perturbed trapezoid inequality, J. Inequal. Pure Appl. Math., 3(2) (2002), Article ID 29.
- [5] Z. Liu, Some inequalities of perturbed trapezoid type, J. Inequal. Pure Appl. Math., 7(2) (2006), Article ID 47.
- [6] H. Budak, H. Kara, F. Hezenci, M. Z. Sarıkaya, New parameterized inequalities for twice differentiable functions, Filomat, 37(12) (2023), 3737-3753. https://doi.org/10.2298/FIL2312737B
- [7] A. Kashuri, R. Liko, Some new Hermite–Hadamard type integral inequalities for twice differentiable mappings and their applications, In D. Andrica, T. M. Rassias (Eds.), Differential and Integral Inequalities, Springer, 2019, pp. 459-479.
- [8] J. Park, Hermite-Hadamard-like type inequalities for twice differentiable convex functions, International Journal of Mathematical Analysis, 8(59) (2014), 2909-2926. http://dx.doi.org/10.12988/ijma.2014.411377
- [9] H. D. Desta, H. Budak, H. Kara, New perspectives on fractional Milne-type inequalities: Insights from twice-differentiable functions, Univ. J. Math. Appl., 7(1) (2024), 30-37. https://doi.org/10.32323/ujma.1397051
- [10] M. Z. Sarıkaya, S. Erden, H. Budak, On the generalized integral inequalities for twice differentiable mappings, Sigma Journal of Engineering and Natural Sciences, 37(1) (2019), 187-205.
