... CorporationJournal of Inequalities and ApplicationsVolume 2008, Article ID 717614, 14 pagesdoi:10.1155/2008/717614 Research Article A Refinement of Jensen’s Inequality for a Class of Increasing and Concave ... admissible q, t,andx1.8 Journal of Inequalities and ApplicationsLemma 1.3. For any integer n ≥ 1, and for all x1, ,xnwith each xk∈ a, b and all p1, ,pn,where each pk≥ 0 and nk1pk ... as a refinement of Jensen’s inequality for a class of increasing and concave functions. Many other refinementscan be found in 2.Theorem 1.1 see 1. Suppose that xk∈ a, b and pk≥ 0 for...