Generalized Cauchy difference equations. II

Author:
Bruce Ebanks

Journal:
Proc. Amer. Math. Soc. **136** (2008), 3911-3919

MSC (2000):
Primary 39B22

Published electronically:
May 20, 2008

MathSciNet review:
2425731

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The main result is an improvement of previous results on the equation

**1.**J. Aczél,*A short course on functional equations*, Theory and Decision Library. Series B: Mathematical and Statistical Methods, D. Reidel Publishing Co., Dordrecht, 1987. Based upon recent applications to the social and behavioral sciences. MR**875412****2.**Bruce R. Ebanks,*On Heuvers’ logarithmic functional equation*, Results Math.**42**(2002), no. 1-2, 37–41. MR**1934223**, 10.1007/BF03323552**3.**Bruce Ebanks,*Generalized Cauchy difference functional equations*, Aequationes Math.**70**(2005), no. 1-2, 154–176. MR**2167992**, 10.1007/s00010-004-2739-5**4.**B. R. Ebanks, P. L. Kannappan, and P. K. Sahoo,*Cauchy differences that depend on the product of arguments*, Glas. Mat. Ser. III**27(47)**(1992), no. 2, 251–261 (English, with English and Serbo-Croatian summaries). MR**1244642****5.**István Ecsedi,*On the functional equation 𝑓(𝑥+𝑦)-𝑓(𝑥)-𝑓(𝑦)=𝑔(𝑥𝑦)*, Mat. Lapok**21**(1970), 369–374 (1971) (Hungarian, with English summary). MR**0306754****6.**Konrad J. Heuvers,*Another logarithmic functional equation*, Aequationes Math.**58**(1999), no. 3, 260–264. MR**1715396**, 10.1007/s000100050112**7.**Antal Járai,*Regularity properties of functional equations in several variables*, Advances in Mathematics (Springer), vol. 8, Springer, New York, 2005. MR**2130441****8.**Antal Járai, Gyula Maksa, and Zsolt Páles,*On Cauchy-differences that are also quasisums*, Publ. Math. Debrecen**65**(2004), no. 3-4, 381–398. MR**2107955****9.**K. Lajkó,*Special multiplicative deviations*, Publ. Math. Debrecen**21**(1974), 39–45. MR**0364932****10.**Gyula Maksa,*On the functional equation 𝑓(𝑥+𝑦)+𝑔(𝑥𝑦)=ℎ(𝑥)+ℎ(𝑦)*, Publ. Math. Debrecen**24**(1977), no. 1-2, 25–29. MR**0447867****11.**Walter Rudin,*Principles of mathematical analysis*, 3rd ed., McGraw-Hill Book Co., New York-Auckland-Düsseldorf, 1976. International Series in Pure and Applied Mathematics. MR**0385023**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
39B22

Retrieve articles in all journals with MSC (2000): 39B22

Additional Information

**Bruce Ebanks**

Affiliation:
Department of Mathematics and Statistics, P.O. Box MA, Mississippi State University, Mississippi State, Mississippi 39762

Email:
ebanks@math.msstate.edu

DOI:
https://doi.org/10.1090/S0002-9939-08-09379-9

Keywords:
Cauchy difference,
cocycle equation,
functional independence,
Pexider equation,
implicit function theorem,
philandering,
regularity properties,
functional equations

Received by editor(s):
June 28, 2006

Received by editor(s) in revised form:
September 20, 2007

Published electronically:
May 20, 2008

Communicated by:
David Preiss

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.