# Article ID: MTJPAM-D-21-00030

## Title: On a functional equation related to diversity

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00030; Volume 4 / Issue 1 / Year 2022, Pages 37-43

Document Type: Research Paper

Author(s): Poonam Garg a , Shveta Grover b , Dhiraj Kumar Singh c

aDepartment of Mathematics, Deen Dayal Upadhyaya College (University of Delhi), Azad Hind Fauj Marg, Phase 1, Dwarka Sector-3, Dwarka, Delhi 110078, India

bDepartment of Mathematics, University of Delhi, Delhi 110007, India

cDepartment of Mathematics, Zakir Husain Delhi College (University of Delhi), Jawaharlal Nehru Marg, Delhi 110002, India

Received: 3 May 2021, Accepted: 3 September 2021, Published: 25 September 2021.

Corresponding Author: Dhiraj Kumar Singh (Email address: dhiraj426@rediffmail.com, dksingh@zh.du.ac.in)

Full Text: PDF

Abstract

The general solution of the functional equation

$\sum\limits\limits^n_{i=1}\sum\limits\limits^m_{j=1}f\left(p_iq_j\right)=\sum\limits\limits^n_{i=1}k\left(p_i\right)\sum\limits\limits^m_{j=1}q^{\beta }_j\ ,$

where   f,   k   are real valued mappings each having the domain   I = [0, 1];   (p1, …, pn)∈Γn,     (q1, …, qm)∈Γm;   n ≥ 3, m ≥ 2 being fixed integers;   0 < β ∈ ℝ,   β ≠ 1   have been obtained. The relevance of its general solution to the diversity index has been discussed.

Keywords: Additive mapping, sum form functional equation, the entropies of degree β, index of diversity

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