Log-convex solutions of the second order to the functional equation f (x + 1) = g (x) f (x)

Rassias, TM; Trif, T

dc.contributor.author	Rassias, TM	en
dc.contributor.author	Trif, T	en
dc.date.accessioned	2014-03-01T01:56:20Z
dc.date.available	2014-03-01T01:56:20Z
dc.date.issued	2007	en
dc.identifier.issn	0022247X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/28063
dc.subject	Gamma-function	en
dc.subject	Gamma-type functional equation	en
dc.subject	Log-convex functions of higher order	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.identifier.primary	10.1016/j.jmaa.2006.09.060	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jmaa.2006.09.060	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(E)f (x + 1) = g (x) f (x) for all x ∈ 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): Γ-type functions, J. Math. Anal. Appl. 209 (1997) 605-623] and generalize results obtained by L. Lupaş [L. Lupaş, The C-function of E.W. Barnes, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 1 (1990) 5-11]. © 2006 Elsevier Inc. All rights reserved.	en
heal.journalName	Journal of Mathematical Analysis and Applications	en
dc.identifier.doi	10.1016/j.jmaa.2006.09.060	en
dc.identifier.volume	331	en
dc.identifier.issue	2	en
dc.identifier.spage	1440	en
dc.identifier.epage	1451	en