Ulam's problem for approximate homomorphisms in connection with Bernoulli's differential equation

Jung, S-M; Rassias, TM

dc.contributor.author	Jung, S-M	en
dc.contributor.author	Rassias, TM	en
dc.date.accessioned	2014-03-01T01:27:31Z
dc.date.available	2014-03-01T01:27:31Z
dc.date.issued	2007	en
dc.identifier.issn	0096-3003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18490
dc.subject	Bernoulli's differential equation	en
dc.subject	Generalized Hyers-Ulam stability	en
dc.subject	Hyers-Ulam stability	en
dc.subject	Hyers-Ulam-Rassias stability	en
dc.subject	Stability	en
dc.subject	Ulam's problem	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Asymptotic stability	en
dc.subject.other	Computational methods	en
dc.subject.other	Differential equations	en
dc.subject.other	Problem solving	en
dc.subject.other	Bernoulli's differential equation	en
dc.subject.other	Generalized Hyers-Ulam stability	en
dc.subject.other	Hyers-Ulam stability	en
dc.subject.other	Hyers-Ulam-Rassias stability	en
dc.subject.other	Ulam's problem	en
dc.subject.other	Approximation theory	en
dc.title	Ulam's problem for approximate homomorphisms in connection with Bernoulli's differential equation	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.amc.2006.08.120	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.amc.2006.08.120	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	Ulam's problem for approximate homomorphisms and its application to certain types of differential equations was first investigated by Alsina and Ger. They proved in [C. Alsina, R. Ger, On some inequalities and stability results related to the exponential function, J. Inequal. Appl. 2 (1998) 373-380] that if a differentiable function f : I -> R satisfies the differential inequality vertical bar y'(t) - y(t)vertical bar <= epsilon, where I is an open subinterval of R, then there exists a solution f(0) : I R -> of the equation y'(t) = y(t) such that vertical bar(t) - fo(t)vertical bar <= 3 epsilon for any t epsilon I. In this paper, we investigate the Ulam's problem concerning the Bernoulli's differential equation of the form y(t)(-x)y'(t) + g(t)y(t)(1-x) + h(t) = 0. (C) 2006 Elsevier Inc. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	Applied Mathematics and Computation	en
dc.identifier.doi	10.1016/j.amc.2006.08.120	en
dc.identifier.isi	ISI:000246830900028	en
dc.identifier.volume	187	en
dc.identifier.issue	1 SPEC. ISS.	en
dc.identifier.spage	223	en
dc.identifier.epage	227	en