Journal of Inequalities and Applications 
Volume 5 (2000), Issue 3, Pages 263-285
doi:10.1155/S1025583400000138

Inequalities of Furuta and Mond–Pečarić on the Hadamard product

Yuki Seo,1 Sin-El Takahasi,2 Josip Pečarić,3 and Jadranka Mićić4

 1Tennoji Branch, Senior Highschool, Osaka Kyoiku University, Tennoji, Osaka 543-0054, Japan
2Department of Basic Technology, Appfied Mathematics and Physics, Yamagata University, Yonezawa 992-8501, Japan
3Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, Zagreb 10000, Croatia
4Technical College Zagreb, University of Zagreb, Konavoska 2, Zagreb 10000, Croatia
Received 30 April 1999; Revised 10 July 1999

Abstract

As a continuation of (J. Mičić, Y. Seo, S.-E. Takahasi and M. Tominaga, Inequalities of Furuta and Mond–Pečarić, Math. Ineq. Appl., 2 (1999), 83–111), we shall discuss complementary results to Jensen’s type inequalities on the Hadamard product of positive operators, which is based on the idea due to Furuta and Mond–Pečarić. We shall show Hadamard product versions of operator inequalities associated with extensions of Hölder–McCarthy and Kantorovich inequalities established by Furuta, Ky Fan and Mond–Pečarić.