Inequalities for averages of quasiconvex and superquadratic functions
2016 (Engelska)Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, nr 2, s. 535-550Artikel i tidskrift (Refereegranskat) Published
Abstract [en]
For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) are also included.
Ort, förlag, år, upplaga, sidor
2016. Vol. 19, nr 2, s. 535-550
Nationell ämneskategori
Matematisk analys
Forskningsämne
Matematik
Identifikatorer
URN: urn:nbn:se:ltu:diva-10062DOI: 10.7153/mia-19-40ISI: 000374170300009Scopus ID: 2-s2.0-84958824735Lokalt ID: 8d020a5b-4ec5-47c7-b999-5644a2b10659OAI: oai:DiVA.org:ltu-10062DiVA, id: diva2:983002
Anmärkning
Validerad; 2016; Nivå 2; 20160302 (andbra)
2016-09-292016-09-292018-07-10Bibliografiskt granskad