Left-sided Hermite-Hadamard Type Inequalities for Trigonometrically ?-Functions

In this paper, we obtain refinements of the left-sided Hermite-Hadamard inequality for functions whose first derivatives in absolute value are trigonometrically ?-function. Keywords: Convex function, trigonometrically convex function, trigonometrically ?- functions, Hermite-Hadamard inequality

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[1] K. Bekar, "Hermite-Hadamard type inequalities for trigonometrically Pfunctions", C. R. Acad. Bulgare Sci., 72(11), 2019.
[2] 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.
[3] S.S. Dragomir and C.E.M. Pearce, "Selected Topics on Hermite-Hadamard Inequalities and Its Applications", RGMIA Monograph 2002.
[4] S.S. Dragomir, J. Pečarić and LE.Persson, "Some inequalities of Hadamard Type", Soochow J. Math., 21 (3)(2001), pp. 335- 341.
[5] J. Hadamard, "Étude sur les propriétés des fonctions entières en particulier d’une fonction considérée par Riemann", J. Math. Pures Appl. 58(1893), 171-215.
[6] İ. İşcan, "New refinements for integral and sum forms of Hölder inequality", J. Inequal. Appl., (2019) 2019:304, 11 pages.
[7] İ. İşcan and M. Kunt, "Hermite-HadamardFejer type inequalities for quasi geometrically convex functions via fractional integrals", J. Math., Volume 2016, Article ID 6523041, 7 pages.
[8] H. Kadakal, "Hermite-Hadamard type inequalities for trigonometrically convex functions", Sci. Stud. Res. Ser. Math. Inform., Vol. 28(2018), No. 2, 19-28.
[9] M. Kadakal, H. Kadakal and İ. İşcan, "Some new integral inequalities for ?-times differentiable ?-convex functions in the first sense", TJANT, Vol. 5, No. 2 (2017), 63-68.
[10] U.S., Kırmacı, "Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula", Appl. Math. Comput. 147 (1) (2004), 137-146.
[11] S. Maden, H. Kadakal, M. Kadakal and İ, İşcan, "Some new integral inequalities for ?-times differentiable convex and concave functions", J. Nonlinear Sci. Appl., 10, 12(2017), 6141-6148.
[12] S. Özcan, and İ. İşcan, "Some new HermiteHadamard type inequalities for s-convex functions and their applications", J. Inequal. Appl., Article number: 2019:201 (2019).
[13] S. Varošanec, "On ℎ-convexity", J. Math. Anal. Appl. 326 (2007) 303-311.
[14] G. Zabandan, "A new refinement of the Hermite-Hadamard inequality for convex functions", J. Inequal. Pure Appl. Math. 10 2(2009), Article ID 45.