Huriye KADAKAL

Some integral inequalities for multiplicatively geometrically P -functions

In this manuscript, by using a general identity for differentiable functions wecan obtain new estimates on a generalization of Hadamard, Ostrowski andSimpson type inequalities for functions whose derivatives in absolute value atcertain power are multiplicatively geometrically P -functions. Some applica-tions to special means of real numbers are also given.

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Dragomir, S.S. and Pearce, C.E.M. (2000). Selected Topics on Hermite-Hadamard In- equalities and Applications, RGMIA Mono- graphs, Victoria University, 2000.
Dragomir, S.S. and Rassias, Th. M. (2002). Ostrowski type inequalities and applications in numerical integration. Kluwer Academic Pub- lishers, Dordrecht, Boston, London.
Dragomir, S.S. Pečarić, J. and Persson, L.E. (1995). Some inequalities of Hadamard type. Soochow Journal of Mathematics, 21(3), 335- 341.
Kadakal, H. (2018). Multiplicatively P - functions and some new inequalities. New Trends in Mathematical Sciences, 6(4), 111- 118.
İşcan, İ., Numan, S. and Bekar, K. (2014). Hermite-Hadamard and Simpson type in- equalities for differentiable harmonically P - functions. British Journal of Mathematics & Computer Science, 4(14), 1908-1920.
Kadakal, H., Maden, S., Kadakal M. and İşcan, İ. (2017). Some new integral inequali- ties for n-times differentiable P -functions. In- ternational Conference on Advances in Nat- ural and Applied Sciences, Antalya, Turkey, 18-21 April 2017.
Kadakal, M., Turhan, S. Maden S. and İşcan, İ. (2018). Midpoint type inequalities for the multiplicatively P -functions. Interna- tional Conference on Mathematics and Math- ematics Education, ICMME-2018, Ordu Uni- versity, Ordu, 27-29 June 2018.
Pearce, C.E.M. and Rubinov, A.M. (1999). P -functions, quasi-convex functions and Hadamard-type inequalities. Journal of Mathematical Analysis and Applications, 240, 92–104.
Kadakal, M., Karaca, H. and İşcan, İ. (2018). Hermite-Hadamard type inequali- ties for multiplicatively geometrically P- functions. Poincare Journal of Analysis & Applications, 2018(2(I)), 77-85.
İşcan, İ. (2014). Hermite-Hadamard type inequalities for GA-s-convex functions, Le Matematiche, Vol. LXIX-Fasc. II, 129–146.