Abstract
The Hermite polynomial and Green function are used to constructthe identities related to majorization type inequalities for convex function. By using Cebysev functional the bounds for the new identities are found to develop the Gruss and Ostrowski type inequalities. Further more exponential convexity together with Cauchy means is presented for linear functionals associated with the obtained inequalities.DOI : http://dx.doi.org/10.22342/jims.22.1.251.1-25
Highlights
The function G is convex in s, it is symmetric, so it is convex in t
In order to recall the definition of n−convex function, first we write the definition of divided difference
We present generalized majorization inequalities and in particular we discuss the results for (m, n − m) interpolating polynomial, two-point Taylor interpolating polynomial
Summary
We begin this section with the proof of some identities related to generalizations of majorization inequality. Let −∞ < α = a1 < a2 · · · < ar = β < ∞, (r ≥ 2) be the given points, w = (w1, ..., wm), x = (x1, ..., xm) and y = (y1, ..., ym) be m-tuples such that xl, yl ∈ [α, β], wl ∈ R (l = 1, ..., m) and Hij, G be as defined in (12) and (9) respectively. Let −∞ < α = a1 < a2 · · · < ar = β < ∞, (r ≥ 2) be given points and x, y : [a, b] → [α, β], w : [a, b] → R be continuous functions and Hij and G be as defined in (12) and (9) respectively. In the following theorem we give generalized majorization integral inequality. If the inequality (reverse inequality) in (41) holds and the function F (.) is non negative (non positive), the right hand side of (41) will be non negative (non positive) that is the inequality (reverse inequality) in (8) will hold
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
