MAJORIZATION TYPE INEQUALITIES VIA GREEN FUNCTION AND HERMITE'S POLYNOMIAL

M. Adil Khan, N. Latif, J. Pecaric


Abstract


The Hermite polynomial and Green function are used to construct
the 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


Keywords


Majorization theorem; Hermite's interpolating polynomial; (m; n -m) interpolating polynomial; two-point Taylor interpolating polynomial; Cebysev functional; nexponentially convex function; mean value theorems; Stolarsky type means.

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p-ISSN:2086-8952e-ISSN:2460-0245