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
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.
Full Text: PDF
The general solution of the functional equation
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 diversityReferences:
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