{"id":"hexagon/2610.00463","pdf":"https://hexagonmath.org/pdf/2610.00463v1","url":"https://hexagonmath.org/abs/2610.00463v1","tags":["math.CV","msc:30C10","msc:11C08","msc:11S05","Dubinin-Sugawa dual mean value theorem","Non-Archimedean field.","Smale mean value theorem"],"score":0,"title":"Non-Archimedean Smale Mean Value and Dubinin–Sugawa Dual Mean Value Problems","domain":"math.NT","source":"hexagon","authors":["K. MAHESH KRISHNA"],"reviews":0,"subject":"math.NT","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}