
Journal of Convex Analysis 29 (2022), No. 1, 205220 Copyright Heldermann Verlag 2022 Some Integral Inequalities for Arithmetically and Geometrically Convex Functions of Two Variables Vahid Darvish School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China vahid.darvish@mail.com Tahere A. Roushan Dept. of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran t.roushan@umz.ac.ir Svetlin G. Georgiev Sorbonne University, Paris, France svetlingeorgiev1@gmail.com Sever S. Dragomir Dept. of Mathematics, School of Engineering and Science,, Victoria University, Melbourne, Australia sever.dragomir@vu.edu.au We introduce arithmeticgeometrically and geometricgeometrically convex functions for two variables. Then, we prove HermiteHadamard type inequalities for these functions. As applications, some new inequalities for unitarily invariant norms are established. Keywords: HermiteHadamard inequality, convex function, arithmeticgeometrically convex, unitarily invariant norm. MSC: 47A63, 15A60, 47B05, 47B10, 26D15. [ Fulltextpdf (118 KB)] for subscribers only. 