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

Yıl 2020, , 487 - 493, 01.06.2020

Kerim Bekar

https://doi.org/10.16984/saufenbilder.672838

Öz

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

Anahtar Kelimeler

Convex function, trigonometrically convex function, trigonometrically P-functions, Hermite-Hadamard inequality

Kaynakça

• K. Bekar, "Hermite-Hadamard type inequalities for trigonometrically P-functions", Comptes rendus de l’Academie bulgare des Sciences, 72(11), 2019.
• 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.
• S.S. Dragomir and C.E.M. Pearce, "Selected Topics on Hermite-Hadamard Inequalities and Its Applications", RGMIA Monograph 2002.
• S.S. Dragomir, J. Pečarić and LE.Persson, "Some inequalities of Hadamard Type", Soochow Journal of Mathematics, 21 (3)(2001), pp. 335-341.
• 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.
• İ. İşcan, "New refinements for integral and sum forms of Hölder inequality", Journal of Inequalities and Applications, (2019) 2019:304, 11 pages.
• İ. İşcan and M. Kunt, "Hermite-Hadamard-Fejer type inequalities for quasi geometrically convex functions via fractional integrals", Journal of Mathematics, Volume 2016, Article ID 6523041, 7 pages.
• H. Kadakal, "Hermite-Hadamard type inequalities for trigonometrically convex functions", Scientific Studies and Research. Series Mathematics and Informatics, Vol. 28(2018), No. 2, 19-28.
• M. Kadakal, H. Kadakal and İ. İşcan, "Some new integral inequalities for n-times differentiable s-convex functions in the first sense", Turkish Journal of Analysis and Number Theory, Vol. 5, No. 2 (2017), 63-68.
• U.S., Kırmacı, "Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula", Applied Mathematics and Computation 147 (1) (2004), 137-146.
• S. Maden, H. Kadakal, M. Kadakal and İ, "Some new integral inequalities for n-times differentiable convex and concave functions", Journal of Nonlinear Sciences and Applications, 10, 12(2017), 6141-6148.
• S. Özcan, and İ. İşcan, "Some new Hermite-Hadamard type inequalities for s-convex functions and their applications", Journal of Inequalities and Applications, Article number: 2019:201 (2019).
• S. Varošanec, "On h-convexity", J. Math. Anal. Appl. 326 (2007) 303-311.
• G. Zabandan, "A new refinement of the Hermite-Hadamard inequality for convex functions", J. Inequal. Pure Appl. Math. 10 2(2009), Article ID 45.