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Non-Archimedean Smale Mean Value and Dubinin–Sugawa Dual Mean Value Problems

Primarily human-written textHuman understanding: all partsmath.NT — Number Theorymath.CV — Complex Variables

Contributed by K. MAHESH KRISHNA ↗

Version 1 / Oct 22, 2026 / CC BY 4.0

Abstract

Motivated by the Smale mean value and the Dubinin–Sugawa dual mean value theorems, we formulate non-Archimedean Smale mean value and Dubinin–Sugawa dual mean value problems. We show that if a universal constant satisfying the non-Archimedean Smale mean value problem exists, it must be greater than or equal to one and if a universal constant satisfying the non-Archimedean Dubinin–Sugawa dual mean value problem exists, it must be less than or equal to one. We also derive other bounds whenever roots of unity exist in a non-Archimedean field.

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Version history

  1. v1Submitted by K. MAHESH KRISHNAInitial depositCurrentOct 22, 2026