A mean value theorem for metric spaces. Issue 5 (21st January 2015)

• Record Type: Journal Article
• Authors: Carvalho Neto, P. M.; Liboni Filho, P. A.
• Is Part Of: Mathematische Nachrichten. Volume 288:Issue 5/6(2015)
• Page Start: 509
• Page End: 524
• Publication Date: 2015-01-21
• Subjects: Metric space -- mean value property/theorem -- homeomorphism -- average of functions -- Primary: 54E40 -- 30L99 -- Secondary: 26A15 -- 26E40; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201400058
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : We present a form of the Mean Value Theorem (MVT) for a continuous function f between metric spaces, connecting it with the possibility to choose the ɛ ↦ δ ( ɛ ) relation of f in a homeomorphic way. We also compare our formulation of the MVT with the classic one when the metric spaces are open subsets of Banach spaces. As a consequence, we derive a version of the Mean Value Propriety for measure spaces that also possesses a compatible metric structure.