MAJORIZATION TYPE INEQUALITIES VIA GREEN FUNCTION AND HERMITE'S POLYNOMIAL

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

doi:10.22342/jims.22.1.251.1-25

M. Adil Khan ⁽¹⁾ , N. Latif ⁽²⁾ , J. Pecaric ⁽³⁾

(1) Department of Mathematics, University of Peshawar, Pakistan,

(2) Department of Mathematics, Govt. College University, Pakistan,

(3) Faculty of Textile Technology, University of Zagreb, Croatia

https://doi.org/10.22342/jims.22.1.251.1-25

Issue
Volume 22 Number 1 (April 2016)

Submitted
July 10, 2015

Accepted
November 19, 2015

Published
May 3, 2016

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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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

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Authors

M. Adil Khan

Department of Mathematics, University of Peshawar

adilswati@gmail.com (Primary Contact)

N. Latif

Department of Mathematics, Govt. College University

J. Pecaric

Faculty of Textile Technology, University of Zagreb

Khan, M. A., Latif, N., & Pecaric, J. (2016). MAJORIZATION TYPE INEQUALITIES VIA GREEN FUNCTION AND HERMITE’S POLYNOMIAL. Journal of the Indonesian Mathematical Society, 22(1), 1–25. https://doi.org/10.22342/jims.22.1.251.1-25