A Refinement of the Integral Jensen Inequality Pertaining Certain Functions with Applications. (30th July 2022) - Sayed, Zaid Mohammed Mohammed Mahdi; Adil Khan, Muhammad; Khan, Shahid; Pečarić, Josip
Abstract : In this paper, we present a new refinement of the integral Jensen inequality by utilizing certain functions and give its applications to various means. We utilize the refinement to obtain some new refinements of the Hermite-Hadamard and Hölder's inequalities as well. Also, we present its applications in information theory. At the end of this paper, we give a more general form of the proposed refinement of the Jensen inequality, associated to several functions.