On Hermite-Hadamard type inequalities for functions whose first derivative absolute values are convex and concave

• Autorzy: Qaisar S. , Hussain S.

Identyfikatory

DOI

10.1515/fascmath-2017-0011

• Języki publikacji: EN

Abstrakty

EN

In this paper, we derive general integral identity by establishing new Hermite-Hadamard type inequalities for functions whose absolute values of derivatives are convex and concave. Corresponding error estimates for midpoint formula are also included. Moreover, some applications to special means of real numbers are also provided.

Słowa kluczowe

EN

Hermite-Hadamard inequality; convex functions; special means; midpoint formula; Holder's inequality; power mean inequality

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2017
• Tom: Nr 58
• Strony: 155--166
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Qaisar S.

• Department of Mathematics, COMSATS Institute of Information Technology, Sahiwal, Pakistan

autor

Hussain S.

• Department of Mathematics, College of Science, Qassim University, Buraydah 51428, Saudi Arabia

Bibliografia

• [1] Avci M., Kavurmaci H., Ozdemir M.E., New inequalities of Hermite-Hadamard type via s-convex functions in the second sense with applications, Appl. Math. Comput., 217(2011), 5171-5176.
• [2] Dragomir S.S., Pearce C.E.M., Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs, Victoria University, 2000, http://www.sta.vu.edu.au/RGMIA/monographs/hermite−hadamard.html.
• [3] Hussain S., Bhatti M.I., Iqbal M., Hadamard-type inequalities for s-convex functions I, Punjab Univ. Jour. Math., 41(2009), 51-60.
• [4] Hussain S., Qaisar S., More results on Hermite-Hadamard type inequality through (α, m)-preinvexity, J. Appl. Anal. Comput., 6(2)(2016), 293-305.
• [5] Kirmaci U.S., Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comp., 147 (2004), 137-146.
• [6] Kavurmaci H., Avci M., Ozdemir M.E., New inequalities of Hermite-Hadamard type for convex functions with applications, JIA, 86(2011).
• [7] Qaisar S., Hussain S., He C., On new inequalities of Hermite-Hadamard type for generalized convex functions, Italian Journal of Pure and Applied Mathematics, 33(2014), 139-148.
• [8] Qaisar S., Hussain S., He C., On new inequalities of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex with applications, Journal of the Egyptian Mathematical Society, 22(1)(2014), 19-22.
• [9] Pearce C.E.M., Pecaric J., Inequalities for differentiable mappings with application to special means and quadrature formula, Appl. Math. Lett., 13(2000), 51-55.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).