**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}

^{a}Department of Mathematics, Deen Dayal Upadhyaya College (University of Delhi), Azad Hind Fauj Marg, Phase 1, Dwarka Sector-3, Dwarka, Delhi 110078, India

^{b}Department of Mathematics, University of Delhi, Delhi 110007, India

^{c}Department 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

where *f*, *k* are real valued mappings each having the domain *I = [0, 1]*; (*p*_{1}, …, *p*_{n})∈*Γ*_{n}, (*q*_{1}, …, *q*_{m})∈*Γ*_{m}; *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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