Abstract and Applied Analysis

Solution of Several Functional Equations on Nonunital Semigroups Using Wilson’s Functional Equations with Involution

Jaeyoung Chung and Prasanna K. Sahoo

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Abstract

Let S be a nonunital commutative semigroup, σ : S S an involution, and C the set of complex numbers. In this paper, first we determine the general solutions f , g : S C of Wilson’s generalizations of d’Alembert’s functional equations   f x + y + f x + σ y = 2 f ( x ) g ( y ) and f x + y + f x + σ y = 2 g ( x ) f ( y ) on nonunital commutative semigroups, and then using the solutions of these equations we solve a number of other functional equations on more general domains.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 463918, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277177

Digital Object Identifier
doi:10.1155/2014/463918

Mathematical Reviews number (MathSciNet)
MR3256249

Zentralblatt MATH identifier
07022431

Citation

Chung, Jaeyoung; Sahoo, Prasanna K. Solution of Several Functional Equations on Nonunital Semigroups Using Wilson’s Functional Equations with Involution. Abstr. Appl. Anal. 2014 (2014), Article ID 463918, 9 pages. doi:10.1155/2014/463918. https://projecteuclid.org/euclid.aaa/1412277177


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