Jensen, Hölder, Minkowski, Jensen-Steffensen and Slater-Pečarić inequalities derived through N-quasiconvexity

On the Jensen-Steffensen inequality for generalized convex functions

Jensen–Steffensen type inequalities for P -convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of Čebyšev’s inequality and several variants of Hölder’s inequality with weights satisfying the conditions as in the Jensen–Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized.

On the refinements of the Jensen-Steffensen inequality

* Correspondence: [email protected] Abdus Salam School of Mathematical Sciences, GC University, 68-b, New Muslim Town, Lahore 54600, Pakistan Full list of author information is available at the end of the article Abstract In this paper, we extend some old and give some new refinements of the JensenSteffensen inequality. Further, we investigate the log-convexity and the exponential conve...

Normalized Jensen Functional, Superquadracity and Related Inequalities

In this paper we generalize the inequality MJn (f,x,q) ≥ Jn (f,x,p) ≥ mJn (f,x,q) where Jn (f,x,p) = n ∑ i=1 pif (xi)− f ( n ∑ i=1 pixi ) , obtained by S.S. Dragomir for convex functions. We provide cases where we can improve the bounds m and M for convex functions, and also, we show that for the class of superquadratic functions nonzero lower bounds of Jn (f,x,p)− mJn (f,x,q) and nonzero upper...

Inequalities of Jensen-pečarić-svrtan-fan Type

By using the theory of majorization, the following inequalities of Jensen-PečarićSvrtan-Fan type are established: Let I be an interval, f : I → R and t ∈ I, x, a, b ∈ I. If a1 ≤ · · · ≤ an ≤ bn ≤ · · · ≤ b1, a1 +b1 ≤ · · · ≤ an +bn; f(t) > 0, f ′(t) > 0, f ′′(t) > 0, f ′′′(t) < 0 for any t ∈ I, then f(A(a)) f(A(b)) = fn,n(a) fn,n(b) ≤ · · · ≤ fk+1,n(a) fk+1,n(b) ≤ fk,n(a) fk,n(b) ≤ · · · ≤ f1,n...

Jensen Polynomials and the Turan and Laguerre Inequalities