A local mean value theorem for functions on non-Archimedean field extensions of the real numbers

DOI10.1134/S2070046616020059zbMath1345.26042OpenAlexW2397726031MaRDI QIDQ2628825

Khodr Shamseddine, G. Bookatz

Publication date: 18 July 2016

Published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s2070046616020059

zbMATH Keywords

mean value theoreminverse function theoremintermediate value theoremlocally uniformly differentiable functionsnon-Archimedean ordered fieldnon-Archimedean calculus

Mathematics Subject Classification ID

Non-Archimedean analysis (26E30)

Related Items (3)

On Non-Archimedean Valued Fields: A Survey of Algebraic, Topological and Metric Structures, Analysis and Applications ⋮ A weaker smoothness criterion for the inverse function theorem, the intermediate value theorem, and the mean value theorem in a non-Archimedean setting ⋮ Calculus on a non-Archimedean field extension of the real numbers: inverse function theorem, intermediate value theorem and mean value theorem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analysis on the Levi-Civita field and computational applications
• Numerical point of view on calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains
• On locally uniformly differentiable functions on a complete non-Archimedean ordered field extension of the real numbers
• Solving ordinary differential equations on the Infinity Computer by working with infinitesimals numerically
• The implicit function theorem in a non-Archimedean setting
• Higher order numerical differentiation on the infinity computer
• Fields: Algebraically closed and others
• Algebraically Closed Fields Analogous to Fields of Puiseux Series

This page was built for publication: A local mean value theorem for functions on non-Archimedean field extensions of the real numbers