On the General and Measurable Solutions of some Functional Equations

• Autorzy: Prem Nath , Dhiraj Kumar Singh
• Języki publikacji: EN

Abstrakty

EN

The general solutions of two functional equations, without imposing any regularity condition on any of the functions appearing, have been obtained. From these general solutions, the Lebesgue measurable solutions have been deduced by assuming the function(s) to be measurable in the Lebesgue sense. (original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical functions; Functional equation

PL

Matematyka; Funkcje matematyczne; Równanie funkcyjne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2018
• Tom: 32
• Strony: 285--294

Twórcy

autor

Prem Nath

• University of Delhi, India

autor

Dhiraj Kumar Singh

• University of Delhi, India

Bibliografia

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• Losonczi L., Maksa Gy., The general solution of a functional equation in information theory, Glas. Mat. 16(36) (1981), 261-266.
• Maksa Gy., Páles Z., Hyperstability of a class of linear functional equations, Acta Math. Paed. Nyire 17 (2001), 107-112.
• Nath P., On a functional equation and its relevance in information theory, in: Advances in Information Theory and Operations Research, Om Parkash (Ed.), VDM Verlag, Saarbrucken, Germany, 2010, pp. 1-14.
• Nath P., Singh D.K., On a sum form functional equation related to entropies and some moments of a discrete random variable, Demonstratio Math. 42 (2009), no. 1, 83-96.
• Shannon C.E., A mathematical theory of communication, Bell. Syst. Tech. Jour. 27 (1948), 348-423; 623-656.
• Tabor J., Stability of the Cauchy equation with variable bound, Publ. Math. Debrecen 51 (1997), 165-173.

Identyfikatory

DOI

10.1515/amsil-2017-0007