In this paper, some extensions of recent results on Choi-Davis-Jensen’s inequality due to Khosravi et al. [M. Khosravi, J.S. Aujla, S.S. Dragomir, and M.S. Moslehian. Refinements of ChoiDavis-Jensen’s inequality. Bulletin of Mathematical Analysis and Applications, 3:127–133, 2011.] and Fujii et al. [J.-I. Fujii, J. Pečarić, and Y. Seo. The Jensen inequality in an external formula. Journal of Ma...

In this paper, some extensions of recent results on Choi-Davis-Jensen’s inequality due to Khosravi et al. [M. Khosravi, J.S. Aujla, S.S. Dragomir, and M.S. Moslehian. Refinements of ChoiDavis-Jensen’s inequality. Bulletin of Mathematical Analysis and Applications, 3:127–133, 2011.] and Fujii et al. [J.-I. Fujii, J. Pečarić, and Y. Seo. The Jensen inequality in an external formula. Journal of Ma...

Let p be a prime and p1, . . . , pr be distinct prime divisors of p− 1. We prove that the smallest positive integer n which is a simultaneous p1, . . . , pr-power nonresidue modulo p satisfies n < p 1/4−cr+o(1) (p → ∞) for some positive cr satisfying cr = e −(1+o(1))r (r → ∞). Mathematical Subject Classification: 11A15, 11A07, 11N29