A Refined form of the generalized Jensen inequality through an arbitrary function

This article is about a refined form of the generalized Jensen inequality in Riemann sense, which is obtained through a positive integrable function. Then manipulation of certain functions with suitable substitutions in the proposed result enables to establish new refined inequalities for the well-known Hölder, and celebrated Hermite--Hadamard inequalities along with power, and quasi-arithmetic means. Further the proposed result also gives refined estimates to Csiszár divergence and its particular variants.