Complementary inequalities to inequalities of Jensen and Ando based on the Mond-Pečarić method

Applying the Mond-Pečarić method to unital positive linear maps, we shall show several complementary inequalities to Jensen's inequalities on positive linear maps and consequently obtain complementary inequalities to Ando's inequalities associated with operator means. We shall apply them to obtain complementary estimates for the results by Ando, Aujla-Vasudeva and J.I.Fujii on Hadamard product and operator means.