On the Stability of a Sum Form Functional Equation Related to Information Theory

Authors

  • Dhiraj Kumar Singh Department of Mathematics, Zakir Husain Delhi College (University of Delhi), Jawaharlal Nehru Marg, Delhi 110002, India https://orcid.org/0000-0002-5513-9558
  • Shveta Grover Department of Mathematics, Shaheed Bhagat Singh College (University of Delhi), Sheikh Sarai, Phase II, New Delhi 110017, India

DOI:

https://doi.org/10.26713/jims.v18i3.3994

Keywords:

Stability, Additive mapping, Multiplicative mapping, Bounded mapping

Abstract

In this manuscript, we intend to discuss the stability problem of Ulam [29] for a sum form functional equation which appears in the characterization of entropies of degree α proposed by Havrda and Charvát [5].

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References

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[14] P. Nath and D. K. Singh, On a multiplicative type sum form functional equation and its role in information theory, Applications of Mathematics 51(5) (2006), 495 – 516, DOI: 10.1007/s10492-006-0018-6.

[15] P. Nath and D. K. Singh, On a sum form functional equation and its role in information theory, in: Proceedings of the National Conference on ‘Information Technology: Setting Trends in Modern Era’ and 8th Annual Conference of Indian Society of Information Theory and Application (March 18-20, 2006), pp. 88 – 94 (2008).

[16] P. Nath and D. K. Singh, A sum form functional equation related to various entropies in information theory, Glasnik Matematicki 43(1) (2008), 159 – 178.

[17] P. Nath and D. K. Singh, On a sum form functional equation related to entropies and some moments of a discrete random variable, Demonstratio Mathematica 42(1) (2009), 83 – 96, DOI: 10.1515/dema-2009-0109.

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[28] D. K. Singh and S. Grover, On the sum form functional equation related to diversity index, Demonstratio Mathematica 58(1) (2025), 20240075, DOI: 10.1515/dema-2024-0075.

[29] S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York (1960).

[30] G. S. Young, The linear functional equation, The American Mathematical Monthly 65(1) (1958), 37 – 38, DOI: 10.2307/2310306.

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Published

September 25, 2026

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Section

Research Article

How to Cite

Singh, D. K., & Grover, S. (2026). On the Stability of a Sum Form Functional Equation Related to Information Theory. Journal of Informatics and Mathematical Sciences, 18(3), 207-220. https://doi.org/10.26713/jims.v18i3.3994