dc.contributor.author |
Rassias, TM |
en |
dc.contributor.author |
Trif, T |
en |
dc.date.accessioned |
2014-03-01T01:56:30Z |
|
dc.date.available |
2014-03-01T01:56:30Z |
|
dc.date.issued |
2007 |
en |
dc.identifier.issn |
0022-247X |
en |
dc.identifier.uri |
https://dspace.lib.ntua.gr/xmlui/handle/123456789/28129 |
|
dc.subject |
log-convex functions of higher order |
en |
dc.subject |
Gamma-type functional equation |
en |
dc.subject |
Gamma-function |
en |
dc.subject.classification |
Mathematics, Applied |
en |
dc.subject.classification |
Mathematics |
en |
dc.title |
Log-convex solutions of the second order to the functional equation f (x+1)=g (x) f (x) |
en |
heal.type |
journalArticle |
en |
heal.language |
English |
en |
heal.publicationDate |
2007 |
en |
heal.abstract |
In this paper we discuss log-convex solutions of the second order f : R+ -> R+ to the functional equation with initial condition given by f(x+1) g(x)f(x) for all x is an element of R+, f(1) = 1. We prove that if g satisfies an appropriate asymptotic condition, then (E) admits at most one solution f, which is eventually log-convex of the second order. Moreover, f can be defined explicitly in terms of g. If, in addition, g is eventually log-concave of the second order, then (E) has exactly one eventually log-convex of the second order solution. Our results complement similar ones established by R. Webster [R. Webster, Log-convex solutions to the functional equation f (x + 1) = g(x) f (x): Gamma-type functions, J. Math. Anal. Appl. 209 (1997) 605-623] and generalize results obtained by L. Lupas [L. Lupas, The C-function of E.W. Barnes, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 1 (1990) 5-11]. (c) 2006 Elsevier Inc. All rights reserved. |
en |
heal.publisher |
ACADEMIC PRESS INC ELSEVIER SCIENCE |
en |
heal.journalName |
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
en |
dc.identifier.isi |
ISI:000245822600046 |
en |
dc.identifier.volume |
331 |
en |
dc.identifier.issue |
2 |
en |
dc.identifier.spage |
1440 |
en |
dc.identifier.epage |
1451 |
en |