Jensen and Quadratic Functional Equations on Semigroups

Esteban A. Chávez () and Prasanna K. Sahoo ()
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Esteban A. Chávez: Duke University
Prasanna K. Sahoo: University of Louisville

Chapter Chapter 9 in Nonlinear Analysis, 2012, pp 127-145 from Springer

Abstract: Abstract Let S be a commutative semigroup, σ:S→S an endomorphism of order 2, G a 2-cancellative abelian group, and n a positive integer. One of the goals of this paper is to determine the general solutions of the functional equations f 1(x+y)+f 2(x+σy)=f 3(x) and also f 1(x+y)+f 2(x+σy)=f 3(x)+f 4(y) for all x,y∈S n , where f 1,f 2,f 3,f 4:S n →G are unknown functions. The results of this paper improve and generalize the earlier results due to Ebanks, Kannappan, and Sahoo (Can. Math. Bull. 35:321–327, 1992), and Bae and Park (J. Math. Anal. Appl. 326:1142–1148, 2007), and generalize the works of Sinopoulos (Aequ. Math. 59:255–261, 2000).

Keywords: Additive function; Biadditive function; Jensen equation; Quadratic function; Quadratic equation; Functional equation on semigroups; 39B52 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-3498-6_9

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