A method to refine the discrete Jensen’s inequality for convex and mid-convex functions

Estimation of Different Entropies via Taylor One Point and Taylor Two Points Interpolations Using Jensen Type Functionals

“…Pečarić in ( [10,13], see also [11, p. 26]), gave a refinement of Jensen's inequality for convex function. They defined some essential notions to prove the refinement given as follows:…”

“…If the base of log is between 0 and 1, then log is decreasing and therefore inequality in (4.3) are reversed. If λ = 1 and β = 1, we have (ii) and (iii) respectively by taking limit, when λ goes to 1. m,1 ≤ A [10] m,2 ≤ . .…”

A parameter-dependent refinement of the discrete Jensen's inequality for convex and mid-convex functions

“…In a recent work, [4] Horváth and Pečarić define a lot of new sequences, they generalize and give a uniform treatment a number of wellknown results from this area, especially (5) and (6) are extended. Horváth develops a method in [5] to construct decreasing real sequences satisfying (3). His paper contains some improvements of the results in [4] and gives a new approach of the topic.…”

“…His paper contains some improvements of the results in [4] and gives a new approach of the topic. The description of the sequences in [4,5] requires some work, so we do not go into the details. The problem (B) has been considered for the classical Jensen's inequality by Horváth [6].…”

Estimation of different entropies via Lidstone polynomial using Jensen-type functionals

“…Under the assumption of Corollary 4.4 (i), consider the following non-negative functionals: 25 ( f ) = H λ (r) − A [12] m,r , r = 1, . .…”