eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2016-10-31 4 5 140 145 10.12691/tjant-4-5-4 TJANT2016454 article Some New Integral Inequalities for Logarithmically Convex Functions with Applications Ahmet Ocak Akdemir ahmetakdemir@agri.edu.tr 1 Havva Kavurmacı-Önalan 2 Ağrı•İbrahim Çeçen University, Faculty of Science and Arts, Department of Mathematics, Ağrı, Turkey Yüzüncü Yıl University, Education Faculty, Department of Mathematics, Van Turkey In this paper, some new integral inequalities are established for functions whose derivatives in absolute value are logarithmically convex functions by using some useful equalities which were proven by Tseng et al.. Several new estimations are also given in numerical integration. http://pubs.sciepub.com/tjant/4/5/4/tjant-4-5-4.pdf power mean inequality logarithmically convex trapezoidal formula midpoint formula