### NEW TRAPEZOID TYPE INEQUALITIES FOR DIFFERENTIABLE FUNCTIONS

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#### Abstract

In this paper, we first establish that an identity involving generalized fractional integrals for twice differentiable functions. By using this equality, we obtain some trapezoid type inequalities for the functions whose second derivatives in absolute value are convex.

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M. A. Ali, H. Kara, J. Tariboon, S. Asawasamrit, H. Budak and F. Hezenci: Some new Simpson's formula type inequalities for twice differentiable convex functions via generalized fractional operators, Symmetry, 13(12) (2021), Art. 2249.

M. A. Ali, N. Alp, H. Budak and P. Agarwal: On some new trapezoidal inequalities for qb-quantum integrals via Green function. J Anal 30 (2022), 15-33.

A. Barani, S. Barani and S. S. Dragomir: Renements of Hermite-Hadamard type inequality for functions whose second derivatives absolute values are quasi convex. RGMIA Res. Rep. Coll 14 (2011).

A. Barani, S. Barani and S. S. Dragomir: Renements of Hermite-Hadamard inequalities for functions when a power of the absolute value of the second derivative is P-convex, Journal of Applied Mathematics 2012 (2012), Article ID 615737.

H. Budak, H. Kara and F. Hezenci: Fractional Simpson type inequalities for twice differentiable functions, Sahand Communications in Mathematical Analysis, in press.

H. Budak and P. Agarwal: New generalized midpoint type inequalities for fractional integral, Miskolc Mathematical Notes, 20(2) (2019), 781-793.

H. Budak and R. Kapucu: New generalization of midpoint type inequalities for fractional integral, An. Stiint. Univ Al. I. Cuza Iasi. Mat. (N.S) 67(1) (2021).

V. Ciobotariu-Boer: On Some Common Generalizations of two classes of integral inequalities for twice differentiable functions 1 (2018), 43-50.

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 (5) (1998), 91-95.

F. Hezenci, H. Budak, and H. Kara: New version of Fractional Simpson type inequalities for twice differentiable functions, Advances in Difference Equations 460 (2021), 1-10.

M. Iqbal, S. Qaisar and M. Muddassar: A short note on integral inequality of type Hermite-Hadamard through convexity, J. Computational analysis and applications 21(5) (2016) 946-953.

I. Iscan: Hermite-Hadamard and Simpson-like type inequalities for differentiable harmonically convex functions, Journal of Mathematics (2014) Article ID 346305, 10 pages.

U. S. Kirmaci: Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comput. 147(5) (2004), 137-146.

P. O. Mohammed and M. Z. Sarikaya: On generalized fractional integral inequalities for twice differentiable convex functions, Journal of Computational and Applied Mathematics 372 (2020), 112740.

K. Mehrez and P. Agarwal: New Hermite{Hadamard type integral inequalities for convex functions and their applications, Journal of Computational and Applied Mathematics 350 (2019), 274-285.

P. Neang, K. Nonlaopon, J. Tariboon, S. K. Ntouyas and P. Agarwal: Some trapezoid and midpoint type inequalities via fractional (p, q)-calculus, Advances in Difference Equations 2021(1) (2021), Art. 333.

S. Qaisar and S. Hussain: On hermite-hadamard type inequalities for functions whose rst derivative absolute values are convex and concave, Fasciculi Mathematici 58(1) (2017), 155-166.

M. Z. Sarikaya and N. Aktan: On the generalization of some integral inequalities and their applications, Mathematical and Computer Modelling 54(9-10) (2011), 2175-2182.

M. Z. Sarikaya and F. Ertugral: On the generalized Hermite-Hadamard inequalities, Annals of the University of Craiova-Mathematics and Computer Science Series 47(1) (2020), 193-213.

M. Z. Sarikaya, E. Set, H. Yaldiz and N. Basak: Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math Comput Model 57 (9-10) (2013), 2403-2407.

M. Tomar, E. Set and M. Z. Sarkaya: Hermite-Hadamard type Riemann-Liouville fractional integral inequalities for convex functions, AIP Conf. Proc. 1726 (2016), 020035.

DOI: https://doi.org/10.22190/FUMI220104024Y

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