Fractional Hermite-Hadamard Type Inequalities in Information Theory via Interval Calculus

Abstract

This thesis applies interval-valued analysis to information theory by using interval calculus to obtain fractional versions of information inequalities for convex functions. A novel center radius (cr)-order relation is introduced. The P-superquadratic variants of Hermite- Hadamard, Jensen’s, Jensen-Mercer inequalities along with their fractional extensions are further investigated and represented in interval-valued form. By proposing modifications to HH ¡-divergence inequalities for convex functions, information inequalities are also linked to contemporary studies. These efforts provide interval-valued estimates for a range of divergence metrics including Kullback-Leibler, Hellinger and c2.