Open Access Open Access  Restricted Access Subscription or Fee Access

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

Praphull Chhabra

Abstract



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.

Keywords


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

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.