Nondiscrete mathematical induction and iterative existence proofs

DOI10.1016/0024-3795(76)90098-7zbMath0323.46005OpenAlexW2084344008MaRDI QIDQ1224265

Vlastimil Pták

Publication date: 1976

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(76)90098-7

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Fixed-point theorems (47H10) Other ``topological linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) (46A19) Open mapping and closed graph theorems; completeness (including (B)-, (B_r)-completeness) (46A30) Proof theory and constructive mathematics (03F99)

Related Items (17)

Newton's method for a class of nonsmooth functions ⋮ On superadditive rates of convergence ⋮ Infinite products of relations, set-valued series and uniform openness of multifunctions ⋮ Improved error bounds for the modified secant method ⋮ Sharp error bounds for Newton's process ⋮ A remark on small divisors problems ⋮ An error analysis for the secant method ⋮ Error for the modified secant method ⋮ A generalization of regula falsi ⋮ Unnamed Item ⋮ Unnamed Item ⋮ What should be a rate of convergence ? ⋮ A rate of convergence ⋮ Unnamed Item ⋮ Extending the applicability of Newton’s method using nondiscrete induction ⋮ On a class of modified newton processes ⋮ Iterative processes and open mapping theorems

Cites Work

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• A theorem of the closed graph type
• On the closed graph theorem
• A remark on transitivity of operator algebras
• A quantitative refinement of the closed graph theorem

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