Non-isolated, non-strictly monotone points of iterates of continuous functions

DOI10.14321/realanalexch.46.1.0051zbMath1483.26003OpenAlexW4293509737MaRDI QIDQ2054549

Rajendran Palanivel, Veerapazham Murugan

Publication date: 3 December 2021

Published in: Real Analysis Exchange (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/real-analysis-exchange/volume-46/issue-1/Non-isolated-non-strictly-monotone-points-of-iterates-of-continuous/10.14321/realanalexch.46.1.0051.full

zbMATH Keywords

Cantor setiterative rootnon-isolated non-strictly monotone pointsnon-strictly monotone pointsuncountable measure zero dense set

Mathematics Subject Classification ID

Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Iteration theory, iterative and composite equations (39B12) Foundations: limits and generalizations, elementary topology of the line (26A03)

Related Items (3)

Baire functions and non-isolated non-monotone discontinuities ⋮ Hyers-Ulam stability of an iterative equation for strictly increasing continuous functions ⋮ Iterative roots of continuous functions and Hyers-Ulam stability

Cites Work

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• Iterative roots of piecewise monotonic functions of nonmonotonicity height not less than 2
• The question on characteristic endpoints for iterative roots of PM functions
• Iterative roots of non-PM functions and denseness
• Existence of iterative roots for the sickle-like functions
• A note on iterative roots of PM functions
• Functions for which all points are local extrema
• Zur Iteration reeller Funktionen
• The Elements of Cantor Sets
• A Continuous Function That Is Differentiable Only at the Rationals
• Continuous Nowhere Differentiable Functions
• The Prevalence of Continuous Nowhere Differentiable Functions
• PM functions, their characteristic intervals and iterative roots
• Local Extrema and Nonopenness Points of Continuous Functions
• On Certain Dense, Uncountable Subsets of the Real Line
• Monsters in Calculus
• Everywhere Differentiable, Nowhere Monotone, Functions

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