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Inequalities on Jain- Saraswat’s Functional Divergence for 3- Convex Functions

Praphull Chhabra


Several authors had been done a quality work on discriminating (divergence) measures based on the convex or arched functions, but in this article I introduced a concept of 3- convex function based on the divided difference or isolated contrast. Further, new inequalities on Jain- Saraswat`s functional discrimination (2013) have been explained by considering 3- convex function. Also, some interesting relations among many discriminations, like: Contra harmonic mean discrimination, Chi- square discrimination, Triangular discrimination, Harmonic mean discrimination, Relative JS discrimination, Relative AG discrimination etc., have been evaluated by using the obtained inequalities. Also, I explained the infinite series version of the Jain- saraswat`s functional discrimination in terms of the parametric Chi- r discrimination by using the Taylor’s series with both Lagrange’s and Cauchy’s form of remainders.


Index terms: 3- convex function, Divided difference, Jain- Saraswat`s functional discrimination, New information inequalities, Chi- r discrimination, Taylor`s series with remainders.

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