A Refined Jensen Inequality Connected to an Arbitrary Positive Finite Sequence

The prime purpose of this paper is to provide a refinement of Jensen’s inequality in connection with a positive finite sequence. We deal with the refinement for particular cases and point out the relation between the new result with earlier results of Jensen’s inequality. As results, we obtain refinements of the quasi-arithmetic and power mean inequalities. Finally, several results are obtained in information theory with the help of the main results.