Abstract

We introduce arithmetic-geometrically and geometric-geometrically convex functions for two variables. Then, we prove Hermite-Hadamard type inequalities for these functions. As applications, some new inequalities for unitarily invariant norms are established.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Sever S. Dragomir

Dept. of Mathematics, School of Engineering and Science, Victoria University, Melbourne, Australia

sever.dragomir@vu.edu.au

Keywords

  • Hermite-Hadamard inequality
  • convex function
  • arithmetic-geometrically convex
  • unitarily invariant norm

Mathematics Subject Classification

47A63, 15A60, 47B05, 47B10, 26D15

Suggested citation

V. Darvish, T. A. Roushan, S. G. Georgiev, S. S. Dragomir. “Some Integral Inequalities for Arithmetically and Geometrically Convex Functions of Two Variables.” Journal of Convex Analysis 29 (2022), No. 1, 205–220. https://doi.org/10.68381/jca29012

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press.